Question

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.

Answer 1

5 jars of jam and 3 packages of bread mix are in gift basket

Solution:

Let "x" be the number of jars of jam

Let "y" the number of packages of bread mix

Cost of 1 jars of jam = $ 6

Cost of 1 package of bead mix = $ 5

There are 8 items in the basket

Therefore,

number of jars of jam + number of packages of bread mix = 8

x + y = 8 ---------- eqn 1

A gift basket that contains jars of jam and packages of bread mix costs $45

Therefore, we frame a equation as:

number of jars of jam x Cost of 1 jars of jam + number of packages of bread mix x Cost of 1 package of bead mix = 45

$x \times 6 + y \times 5 = 45$

6x + 5y = 45 --------- eqn 2

Let us solve eqn 1 and eqn 2

From eqn 1,

x = 8 - y --------- eqn 3

Substitute eqn 3 in eqn 2

6(8 - y) + 5y = 45

48 - 6y + 5y = 45

y = 48 - 45

y = 3

Substitute y = 3 in eqn 3

x = 8 - 3

x = 5

Thus 5 jars of jam and 3 packages of bread mix are in gift basket