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Algebra I B
4.4 Applications of Linear Systems
Write a system of linear equations for each word problem. Then solve.
1.
The sum of two numbers is 83. The larger number is 11 more than twice the smaller number. Find the
two numbers.
2.
The difference of two numbers is 6. The sum of 2 times the larger number and 3 times the smaller
number is 37. Find the two numbers.
3.
Nakilah is 3 times as old as Anthony. Together the sum of their ages is 56. How old is Nakilah?
4.
Connor is 4 years younger than Brianna. The sum of their ages is 24. How old is Connor?
5.
Ruth’s age is 3 less than twice Mike’s age. The sum of their ages is 57. How old is Mike?
6.
Oatmeal cookies cost $.45 and ice cream bars cost 30 cents each. The group spent $7.35 and bought 20
items. Write a system of linear equations that can be used to find how many cookies (c) and how many
ice cream bars (b) were purchased.
How many cookies were purchased?
7.
Eight grapefruit and one lemon cost $4.60. Then six grapefruit and three lemons cost
$4.80. Write a system of linear equations that can be used to find how much one
grapefruit cost (g) and how much one lemon cost (r).
How much did one grapefruit cost?
8.
The basketball team is fundraising by selling cards for $10 each and wrapping paper for $5 each. John
sold 13 items for a total of $85. Write a system of linear equations that can be used to find how many
cards (c) and how many packages of wrapping paper (p) John sold.
How many packages of wrapping paper did John sell?
Algebra I B
4.4 Homework
Write a system of linear equations for each word problem. Then solve.
1.
The sum of two numbers is 21. The larger number is 6 less than twice the smaller number. Find the two
numbers.
2.
The difference of two numbers is 15. The larger number is 1 more than 3 times the smaller number.
Find the two numbers.
3.
William is 3 years older than Charmaine. The sum of 3 times Charmaine’s age and 2 times William’s
age is 76. How old are William and Charmaine?
4.
Alysha is two years younger than Bryce. The sum of their ages is 28. How old is Alysha?
5.
Tyshon’s age is 3 less than three times Cedric’s age. The sum of their ages is 57. How old is Tyshon?
6.
Tickets to the concert were $2.50 for adults and $1 for students. $1200 was collected and 750 tickets
were sold. Write a system of linear equations that can be used to find how many adults (a) and how
many students (b) attended.
How many students attended?
7.
Christian sold tickets to game. Good seats were $5 each and poor seats cost $2 each. 210 people
attended and paid $660. Write a system of linear equations that can be used to find how many good
seats (g) and how poor seats (p) were sold.
How many good seats were sold?
8.
DVD’s cost $5 and CD’s cost $3. Liz bought 50 items and spent $190. Write a system of linear
equations that can be used to find how many DVDs (d) and how many CDs (c) Liz bought.
How many CD’s did Liz buy?