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.
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 \($3.75\).
