A gift basket that contains jars of jam and packages of bread mix costs $45. There are 8 items in the basket. Jars of jam cost $6 each, and packages of bread mix cost $5 each. Write and solve a system of linear equations to find the number of jars of jam and the number of packages of bread mix in the gift basket. Let xx represent the number of jars of jam and let y represent the number of packages of bread mix.

Question

Ernest Henson

Mathematics

7 March, 13:38

A gift basket that contains jars of jam and packages of bread mix costs $45. There are 8 items in the basket. Jars of jam cost $6 each, and packages of bread mix cost $5 each. Write and solve a system of linear equations to find the number of jars of jam and the number of packages of bread mix in the gift basket. Let xx represent the number of jars of jam and let y represent the number of packages of bread mix.

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Answers (1)

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Kyler Jensen · Answer 1

8 items

jams+breadmix=8

x+y=8

total value is 45

value of jam=x times cost per jam=x times 6=6x

value of bread=y times cost per bread=y times 5=5y

total value=bread value+jam value

45=5y+6x

we have

x+y=8

6x+5y=45

solve

multiply first equaton by - 5

-5x-5y=-40

add to first equation

-5x-5y=-40

6x+5y=45 +

1x+0y=5

x=5

subsitute

x+y=8

5+y=8

y=3

5 jars of jam

3 jars of bread mix