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A store is having a sale on almonds and jelly beans. For 3 pounds of almonds and 5 pounds of jelly beans, the total cost is $24. For 9 pounds of almonds and 7 pounds of jelly beans, the total cost is $42. Find the cost for each pound of almonds and each pound of jelly beans.

 Feb 9, 2022
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Let x be the cost for one pound of almond and y be the cost for one pound of jelly bean

Making a system of equations:

 

\(3x + 5y = 24\)

\(9x+7y = 42\)

 

Multiplying the first equation by -3 and we get

 

\(-9x- 15y = -72\)

\(9x +7y = 42\)

 

Then we add both equations together

 

\(y = \frac{30}{8} = \boxed{3.75}\)

 

Then we plug 3.75 in for y in the first equation

 

\(3x + 5(3.75) = 24\)

\(3x + 18.75 = 24\)

\(3x = 5.25\)

\(x = \boxed{1.75}\)

 

So one pound of almond cost \($1.75\) and one pound of jelly bean cost \($3.75\).

 Feb 9, 2022

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