Problem #1
In a stationary store, pencils have one price and pens have another price. Two pencils and three pens cost 78 cents. But three pencils and two pens cost 72 cents. How much does one pencil cost?
Problem #2: 17-2
One loaf of bread and six rolls cost $1.80. At the same price, two loaves of bread and four rolls cost $2.40. How much does one loaf of bread cost?
Problem #3: 41-5
A restaurant has a total of 30 tables which are of two types. The first type seats two people at each table; the second type seats five people at each table. A total of 81 people are seated when all seats are occupied. How many tables for two are there?
Problem #4: 12-4
A dollar was changed into 16 coins consisting of just nickels and dimes. How many coins of each kind were in the change?
Problem #5
From a pile of 100 pennies(P), 100 nickels(N), and 100 dimes(D), select 21 coins which have a total value of exactly $1.00. In your selection you must also use at least one coin of each type. How many coins of each of the three types(P, N, D) should be selected?
Problem #6
A dealer packages marbles in two different box sizes. One size holds 5 marbles and the other size holds 12 marbles. If the dealer packaged 99 marbles and used more than 10 boxes, how many boxes of each size did he use?
Problem #7: 43-5
Barbara has 20 coins consisting of nickles and dimes. If the nickles were dimes and the dimes were nickels, she would have 30 cents more than she has now. How many dimes did she have to begin with?
Problem #8: 46-2
Tickets for a concert cost $2 each for children and $5 each for adults. A group of thirty people consisting of children and adults paid a total of $87 for the concert. How many adults were in the group?
Wednesday, November 30, 2011
Wednesday, November 9, 2011
Math problems for Nov. 11 2011
Problem #1
In the USA, the symbol 5/2 means the 5th month, 2nd day, or May 2. But in England, 5/2 means the fifth day, 2nd month, or February 5. How many days of the year each have the same symbol in both the USA and England?
Problem #2
The product of two numbers is 504 and each of the numbers is divisible by 6. However, neither of the two numbers is 6. What is the larger of the two numbers?
Problem #3
A rectangular garden is 14 ft. by 21 ft. and is bordered by a concrete walk 3 ft. wide as shown below. How many square feet are in the surface area of just the concrete walk?
Problem #4
Four numbers are arranged in order of size and the difference between any two adjacent numbers is the same. Suppose 1/3 is the first and 1/2 is the fourth of these numbers. What are the two numbers between 1/3 and 1/2?
Problem #5
Each o the three diagrams at the right shows a balance of weights using different objects. How many cubes will balance a ball?
In the USA, the symbol 5/2 means the 5th month, 2nd day, or May 2. But in England, 5/2 means the fifth day, 2nd month, or February 5. How many days of the year each have the same symbol in both the USA and England?
Problem #2
The product of two numbers is 504 and each of the numbers is divisible by 6. However, neither of the two numbers is 6. What is the larger of the two numbers?
Problem #3
A rectangular garden is 14 ft. by 21 ft. and is bordered by a concrete walk 3 ft. wide as shown below. How many square feet are in the surface area of just the concrete walk?
Problem #4
Four numbers are arranged in order of size and the difference between any two adjacent numbers is the same. Suppose 1/3 is the first and 1/2 is the fourth of these numbers. What are the two numbers between 1/3 and 1/2?
Problem #5
Each o the three diagrams at the right shows a balance of weights using different objects. How many cubes will balance a ball?
Thursday, October 27, 2011
Math problems for Oct. 27
Problem #1
I am less than 6 feet tall but more than 2 feet tall. My height in inches is a multiple of 7 and is also 2 inches more than a multiple of 6. What is my height in inches?
Problem #2
In the multiplication example below, A nad B represent different digits, AB is a two-digit number and BBB is a three-digit number. (* means multiply). What two-digit number does AB represent?
Problem #3
Tom went to a store and spent one-third of his money. He went to a second store where he spent one-third of what remained, and then had $12 when he left. How much money did he have to begin with at the first store?
Problem #4
The tower below has no gaps. Suppose it is painted red on all exterior sides including the bottom, and then cut into cubes along the indicated lines. How many cubes will each have red paint on just three faces?
Problem #5
A9543B represents a six-digit number in which A and B are digits different from each other. The number is divisible by 11 and also by 8. What digit does A represent?
I am less than 6 feet tall but more than 2 feet tall. My height in inches is a multiple of 7 and is also 2 inches more than a multiple of 6. What is my height in inches?
Problem #2
In the multiplication example below, A nad B represent different digits, AB is a two-digit number and BBB is a three-digit number. (* means multiply). What two-digit number does AB represent?
Problem #3
Tom went to a store and spent one-third of his money. He went to a second store where he spent one-third of what remained, and then had $12 when he left. How much money did he have to begin with at the first store?
Problem #4
The tower below has no gaps. Suppose it is painted red on all exterior sides including the bottom, and then cut into cubes along the indicated lines. How many cubes will each have red paint on just three faces?
Problem #5
A9543B represents a six-digit number in which A and B are digits different from each other. The number is divisible by 11 and also by 8. What digit does A represent?
Wednesday, October 19, 2011
Math problems for Oct. 21 2011
Problem #1
Two cash registers of a store had a combined total of $300. When the manager transferred $15 from one register to the other register, each register then had the same amount. How much did the register with the larger amount have before the transfer was made?
Problem #2
The product of two numbers is 128 and their quotient is 8. What are the numbers?
Problem #3
In the figure below, each number represents the length of the segment which is nearest it. How many square units are in the area of the figure if there is a right angle at each corner of the figure?
Problem #4
In the addition problem below, different letters stand for different digits. AH represents a two-digit number and HEE represents a three-digit number. What number does HEE represent?
Problem #5
Barbara has 20 coins consisting of nickels and dimes. If the nickels were dimes and the dimes were nickels, she would have 30 cents more than she has now. How many dimes did she have to begin with?
Two cash registers of a store had a combined total of $300. When the manager transferred $15 from one register to the other register, each register then had the same amount. How much did the register with the larger amount have before the transfer was made?
Problem #2
The product of two numbers is 128 and their quotient is 8. What are the numbers?
Problem #3
In the figure below, each number represents the length of the segment which is nearest it. How many square units are in the area of the figure if there is a right angle at each corner of the figure?
Problem #4
In the addition problem below, different letters stand for different digits. AH represents a two-digit number and HEE represents a three-digit number. What number does HEE represent?
Problem #5
Barbara has 20 coins consisting of nickels and dimes. If the nickels were dimes and the dimes were nickels, she would have 30 cents more than she has now. How many dimes did she have to begin with?
Tuesday, October 11, 2011
Math problems for October 14 2011
Problem #1
The cost of a book is $1 and a whole number of cents. The total cost of six copies of the book is less than $8. However, the total cost of seven copies of the same book at the same price per book is more than $8. What is the least a single copy of the book could cost?
Problem #2
The sum of all digits in the numbers 34, 35, and 36 is 24 because (3+4)+(3+5)+(3+6)=24. Find the sum of all digits in the first twenty-five counting numbers: 1, 2,3, ..., 23, 24, 25
Problem #3
Alice earned a total of $65 for working five days after school. Each day after the first day, she earned $2 more than she earned the day before. How much did she earn on the first day?
Problem #4
Each of the small boxes in the figure is a square and the area of the figure is 52 square units. How many units are there in the outer perimeter of the figure?
Problem #5
A work team of four people completes half of a job in 15 days. How many days will it take a team of ten people to complete the remaining half of the job? (Assume that each person of both teams works at the same rate as each of the other people.)
The cost of a book is $1 and a whole number of cents. The total cost of six copies of the book is less than $8. However, the total cost of seven copies of the same book at the same price per book is more than $8. What is the least a single copy of the book could cost?
Problem #2
The sum of all digits in the numbers 34, 35, and 36 is 24 because (3+4)+(3+5)+(3+6)=24. Find the sum of all digits in the first twenty-five counting numbers: 1, 2,3, ..., 23, 24, 25
Problem #3
Alice earned a total of $65 for working five days after school. Each day after the first day, she earned $2 more than she earned the day before. How much did she earn on the first day?
Problem #4
Each of the small boxes in the figure is a square and the area of the figure is 52 square units. How many units are there in the outer perimeter of the figure?
Problem #5
A work team of four people completes half of a job in 15 days. How many days will it take a team of ten people to complete the remaining half of the job? (Assume that each person of both teams works at the same rate as each of the other people.)
Wednesday, October 5, 2011
Math problems for October 7 2011
Problem #1
Suppose the time is now 2 o'clock on a twelve-hour clock which runs continuously. What time will it show 1,000 hours from now?
Problem #2
The average of five numbers is 6. If one of the five numbers is removed, the average of the four remaining numbers is 7. What is the value of the number that was removed?
Problem #3
If you start with 3 and count by 7s, you get the terms of the sequence 3, 10, 17, ..., 528 where 3 is the 1st term, 10 is the 2nd term, 17 is the 3rd term, and so forth up to 528 which is Nth term. What is the value of N?
Problem #4
When a counting number is multiplied by itself, the result is a perfect square. For example 1, 4, 9 are perfect squares because 1 x 1 = 1, 2 x 2 = 4, and 3 x 3 = 9. How many perfect squares are less than 10,000?
Problem #5
A restaurant has a total of 30 tables which are of two types. The first type seats two people at each table; the second type seats five people at each table. A total 81 people are seated when all seats are occupied. How many tables for two are there?
Suppose the time is now 2 o'clock on a twelve-hour clock which runs continuously. What time will it show 1,000 hours from now?
Problem #2
The average of five numbers is 6. If one of the five numbers is removed, the average of the four remaining numbers is 7. What is the value of the number that was removed?
Problem #3
If you start with 3 and count by 7s, you get the terms of the sequence 3, 10, 17, ..., 528 where 3 is the 1st term, 10 is the 2nd term, 17 is the 3rd term, and so forth up to 528 which is Nth term. What is the value of N?
Problem #4
When a counting number is multiplied by itself, the result is a perfect square. For example 1, 4, 9 are perfect squares because 1 x 1 = 1, 2 x 2 = 4, and 3 x 3 = 9. How many perfect squares are less than 10,000?
Problem #5
A restaurant has a total of 30 tables which are of two types. The first type seats two people at each table; the second type seats five people at each table. A total 81 people are seated when all seats are occupied. How many tables for two are there?
Tuesday, September 27, 2011
Math problems for September 30 2011
Problem #1
A slow clock loses 3 minutes every hour. Suppose the slow clock and a correct clock both show the correct time at 9 am. What time will the slow clock show when the correct clock shows 10 o'clock the evening of the same day?
Problem #2
The figure below is a 'magic square' with missing entries. When complete, the sum of the four entries in each column, each row, and each diagonal is the same. Find the value of A and the value of B.
Problem #3
The digit 3 is written at the right of a certain two-digit number thus forming a three-digit number. The new number is 372 more than the original two-digit number. What was the original two-digit number?
Problem #4
ABCD is a square with area 16 sq. meters. E and F are midpoints of sides AB and BC, respectively. What is the area of trapezoid AEFC, the shaded region?
Problem #5
Peter agreed to work after school for 8 weeks at a fixed weekly rate. But instead of being given only money, he was to be given $85 and a bicycle. However, Peter worked only 5 weeks at the fixed weekly rate and was given $25 and the bicycle. How much was the bicycle worth?
A slow clock loses 3 minutes every hour. Suppose the slow clock and a correct clock both show the correct time at 9 am. What time will the slow clock show when the correct clock shows 10 o'clock the evening of the same day?
Problem #2
The figure below is a 'magic square' with missing entries. When complete, the sum of the four entries in each column, each row, and each diagonal is the same. Find the value of A and the value of B.
Problem #3
The digit 3 is written at the right of a certain two-digit number thus forming a three-digit number. The new number is 372 more than the original two-digit number. What was the original two-digit number?
Problem #4
ABCD is a square with area 16 sq. meters. E and F are midpoints of sides AB and BC, respectively. What is the area of trapezoid AEFC, the shaded region?
Problem #5
Peter agreed to work after school for 8 weeks at a fixed weekly rate. But instead of being given only money, he was to be given $85 and a bicycle. However, Peter worked only 5 weeks at the fixed weekly rate and was given $25 and the bicycle. How much was the bicycle worth?
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