Word Problems
(Answers below)
Type 1: Age Problems
a) Sheri said to Brandon, "1 year ago I was 23 times your age. In another 9 years, I will be triple your age." How old is each person?
b) The difference between Bob and Rogers age is 15 years. In 7 years, Bob will be twice as old as Roger. How old are they now?
c) A grandfather says to his grandson "Today I am four times as old as you are, but in 7 years i will be three times as old as your age". Find the age of each person.
d) A father said to his son, "Today I am four times as old as you are, but in 14 years I will be twice your age." Find the age of each person.
e) Eight years ago, Pam's age was double that of Natalie's. In 12 years, Natalie's age will be 3/4 that of Pam's age. How old are they now?
f) 19 years ago Jill's mom was 24 times her age. In 3 years Jill's mom will be double her age. Determine Jill's age and her mom's age.
g) Stephen is twice Matthew's age. The difference between their age is 30 years. What are their ages?
h) Today Max is three times as old as Mary. In 13 years Max will be twice Mary's age. How old is each person today?
i) Seven years ago Sara was six times as old as her sister Julie. In sixteen years, Julie will be 5/7 Sara's age. how old is each sister?
j) Five years ago Mark was three times as old as Gabrielle. In five years, he will be twice her age. How old is each person?
Type 2: Money Problems
a) You buy two sweaters and a pair of jeans to complete your work uniform. The total bill comes to $125. Your friend buys one sweater and three pairs of jeans of the same type. Her bill comes to $175. What is the cost of one sweater? What is the cost of one pair of jeans?
b) The attendance at a circus was 40000 people. If a child's ticket costs $3.00 and an adult's ticket costs $5.00, and the total receipts amounted to $170000, how many children and how many adults saw the show?
c) Jaime has 2 different jobs. When she works 8 hours as a math tutor and 12 hours as a cashier at a local store, she earns a total of $361.00. If she works 12 hours doing the tutoring and 5 hours at the store she earns $453.75. What is her hourly wage at each job?
d) A customer at a bar purchased 3 beers and 5 single rum n' cokes. His total bill came to $28.50. At the next table, Mike bought a beer for each of the 4 guys and a rum n' coke for each of the 3 girls. It cost him $25.35. What does the bar charge for a beer and what does the bar charge for a rum n' coke?
e) A patron in a bar can purchase 6 shots and 2 beers for $22.50. For the same price he can buy 4 beers and 2 shots. What is the respective close of a beer and a shot?
f) A school office sells pens and pencils. Anna buys 5 pencils and 2 pens and it costs her $5.25. Michael buys 4 pencils and 8 pens for a total cost of $15.40. What does the school charge for a pencil? What do they charge for a pen?
g) Tanya has some quarters and dimes in her pocket. There are 50 coins in all for a total of $7.25. How many dimes and how many quarters does she have?
h) Benny has some dimes and quarters. She has 30 coins in all for a total of $5.70. How many coins of each type does she have?
i) Zara has $5.00 in her coat pocket. This is made up of 38 coins in the form of dimes and quarters. How many dimes and how many quarters does Zara have?
j) Stef's piggy bank has 50 coins totalling $4.15. The coins are all dimes and nickels. How many dimes and how many nickels are there?
k) Shannon cashes her paycheck which is for $530.00. The bank teller gives her 38 bills, some of which are twenty-dollar bills and some that are ten-dollar bills. How many of each kind of bill does Shannon have?
l) Jessie has $8.45 made up of quarters and nickels. She has 77 coins in all. How many quarters and how many nickels does she have?
Type 3: Number Problems
a) The sum of two numbers is 63 and one of the numbers is double the other. What are the numbers?
b) Find two numbers whose difference is 20 if a third of their sum is 40.
c) The difference between two numbers is 7. One-third of the larger number added to one-quarter of the smaller number is 7. Find the numbers.
d) The difference between two numbers is 13. One-half of the smaller number added to one-third of the larger number is 16. Find the numbers.
e) The difference between two numbers is 18. One-half of the large number added to one-quarter of the smaller number is 21. Find the 2 numbers.
f) Two numbers differ by 52. One is triple the other. What are the two numbers?
g) Two numbers differ by 11. One-sixth of the larger number added to one-fifth of the smaller number also results in 11. Find the 2 numbers.
h) One number is four times another number. The difference between the two numbers is 51. What are the numbers?
Answers:
Type 1: Age Problems
a) Brandon is 2 years old and Sheri is 24 years old
b) Bob is 23 and Roger is 8
c) Grandson is 14, grandfather is 56
d) Son is 7, dad is 28
e) Pam is 28, Nathalie is 18
f) Jill is 20, mom is 43
g) Stephen is 60, Matthew is 30
h) Max is 39, Mary is 13
i) Sara is 19, Julie is 9
j) Mark is 35, Gabrielle is 15
Type 2: Money Problems
a) Sweater: $40 Jeans: $45
b) 25000 Adults; 15000 Children
c) $6.75/hr: Cashier, $35/hr Tutoring
d) beer: $3.75 Rum n' coke: $3.45
e) Shot: $2.25, Beer: $4.50
f) Pencil: $0.35, Pen $1.75
g) 15 Quarters, 35 Dimes
h) 18 Quarters, 12 Dimes
i) 8 Quarters, 30 Dimes
j) 17 Nickels, 33 Dimes
k) 15 $20 Bills, 23 $10 Bills
l) 23 Quarters, 54 Nickels
Type 3: Number problems
a) 21 and 42
b) 50 and 70
c) 8 and 15
d) 14 and 27
e) 16 and 34
f) 26 and 78
g) 25 and 36
h) 17 and 68
(Answers below)
Type 1: Age Problems
a) Sheri said to Brandon, "1 year ago I was 23 times your age. In another 9 years, I will be triple your age." How old is each person?
b) The difference between Bob and Rogers age is 15 years. In 7 years, Bob will be twice as old as Roger. How old are they now?
c) A grandfather says to his grandson "Today I am four times as old as you are, but in 7 years i will be three times as old as your age". Find the age of each person.
d) A father said to his son, "Today I am four times as old as you are, but in 14 years I will be twice your age." Find the age of each person.
e) Eight years ago, Pam's age was double that of Natalie's. In 12 years, Natalie's age will be 3/4 that of Pam's age. How old are they now?
f) 19 years ago Jill's mom was 24 times her age. In 3 years Jill's mom will be double her age. Determine Jill's age and her mom's age.
g) Stephen is twice Matthew's age. The difference between their age is 30 years. What are their ages?
h) Today Max is three times as old as Mary. In 13 years Max will be twice Mary's age. How old is each person today?
i) Seven years ago Sara was six times as old as her sister Julie. In sixteen years, Julie will be 5/7 Sara's age. how old is each sister?
j) Five years ago Mark was three times as old as Gabrielle. In five years, he will be twice her age. How old is each person?
Type 2: Money Problems
a) You buy two sweaters and a pair of jeans to complete your work uniform. The total bill comes to $125. Your friend buys one sweater and three pairs of jeans of the same type. Her bill comes to $175. What is the cost of one sweater? What is the cost of one pair of jeans?
b) The attendance at a circus was 40000 people. If a child's ticket costs $3.00 and an adult's ticket costs $5.00, and the total receipts amounted to $170000, how many children and how many adults saw the show?
c) Jaime has 2 different jobs. When she works 8 hours as a math tutor and 12 hours as a cashier at a local store, she earns a total of $361.00. If she works 12 hours doing the tutoring and 5 hours at the store she earns $453.75. What is her hourly wage at each job?
d) A customer at a bar purchased 3 beers and 5 single rum n' cokes. His total bill came to $28.50. At the next table, Mike bought a beer for each of the 4 guys and a rum n' coke for each of the 3 girls. It cost him $25.35. What does the bar charge for a beer and what does the bar charge for a rum n' coke?
e) A patron in a bar can purchase 6 shots and 2 beers for $22.50. For the same price he can buy 4 beers and 2 shots. What is the respective close of a beer and a shot?
f) A school office sells pens and pencils. Anna buys 5 pencils and 2 pens and it costs her $5.25. Michael buys 4 pencils and 8 pens for a total cost of $15.40. What does the school charge for a pencil? What do they charge for a pen?
g) Tanya has some quarters and dimes in her pocket. There are 50 coins in all for a total of $7.25. How many dimes and how many quarters does she have?
h) Benny has some dimes and quarters. She has 30 coins in all for a total of $5.70. How many coins of each type does she have?
i) Zara has $5.00 in her coat pocket. This is made up of 38 coins in the form of dimes and quarters. How many dimes and how many quarters does Zara have?
j) Stef's piggy bank has 50 coins totalling $4.15. The coins are all dimes and nickels. How many dimes and how many nickels are there?
k) Shannon cashes her paycheck which is for $530.00. The bank teller gives her 38 bills, some of which are twenty-dollar bills and some that are ten-dollar bills. How many of each kind of bill does Shannon have?
l) Jessie has $8.45 made up of quarters and nickels. She has 77 coins in all. How many quarters and how many nickels does she have?
Type 3: Number Problems
a) The sum of two numbers is 63 and one of the numbers is double the other. What are the numbers?
b) Find two numbers whose difference is 20 if a third of their sum is 40.
c) The difference between two numbers is 7. One-third of the larger number added to one-quarter of the smaller number is 7. Find the numbers.
d) The difference between two numbers is 13. One-half of the smaller number added to one-third of the larger number is 16. Find the numbers.
e) The difference between two numbers is 18. One-half of the large number added to one-quarter of the smaller number is 21. Find the 2 numbers.
f) Two numbers differ by 52. One is triple the other. What are the two numbers?
g) Two numbers differ by 11. One-sixth of the larger number added to one-fifth of the smaller number also results in 11. Find the 2 numbers.
h) One number is four times another number. The difference between the two numbers is 51. What are the numbers?
Answers:
Type 1: Age Problems
a) Brandon is 2 years old and Sheri is 24 years old
b) Bob is 23 and Roger is 8
c) Grandson is 14, grandfather is 56
d) Son is 7, dad is 28
e) Pam is 28, Nathalie is 18
f) Jill is 20, mom is 43
g) Stephen is 60, Matthew is 30
h) Max is 39, Mary is 13
i) Sara is 19, Julie is 9
j) Mark is 35, Gabrielle is 15
Type 2: Money Problems
a) Sweater: $40 Jeans: $45
b) 25000 Adults; 15000 Children
c) $6.75/hr: Cashier, $35/hr Tutoring
d) beer: $3.75 Rum n' coke: $3.45
e) Shot: $2.25, Beer: $4.50
f) Pencil: $0.35, Pen $1.75
g) 15 Quarters, 35 Dimes
h) 18 Quarters, 12 Dimes
i) 8 Quarters, 30 Dimes
j) 17 Nickels, 33 Dimes
k) 15 $20 Bills, 23 $10 Bills
l) 23 Quarters, 54 Nickels
Type 3: Number problems
a) 21 and 42
b) 50 and 70
c) 8 and 15
d) 14 and 27
e) 16 and 34
f) 26 and 78
g) 25 and 36
h) 17 and 68