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. let x represent the number of jars of jam and let y represent the number of packages of bread mix.system of equations:

Answer 1

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Define jam and bread mix
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Let the number of jar of jam be x
Let the number of packages of bread mix be y

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Form equations and solve
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x + y = 8 --------------------- (1)
6x + 5y = 45 ---------------- (2)

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Rewrite equation to make x the subject
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x+ y = 8
x = 8 - y ----------------------------(1a)

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Substitute (1a) into (2)
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6(8 - y) + 5y = 45
48 - 6y + 5y = 45
y = 48 - 45
y = 3

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Substitute y = 3 into (1) to find x
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x + 3 = 8
x  = 8 - 3
x = 5

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Find jam and bread mix
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Jars of Jam = x = 5
Packages of bread mix = y = 3

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Answer: Jam = 5 ; bread mix = 3
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