The Mushrooms and 3-Bean Salad
30) If 3 cans of mushrooms and 5 cans of 3-bean salad cost $5.90, and 2 cans
of mushrooms and 4 cans of 3-bean salad cost $4.52, then how much is each
can of mushrooms, and each can of 3-bean salad?
x = can of mushrooms
y = can of 3-bean salad
3x + 5y = 5.90
2x + 4y = 4.52
Eliminate one of the variables by multiplying by a negative
number. We will multiply the bottom equation by -1.5:
3x + 5y = 5.90
-3x -6y = -6.78
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-1y = -0.88
y = 0.88 (a negative divided by a negative equals a positive)
Plug the value of y into the equation to solve for x:
(3x + 5y = 5.90)
3x + 4.40 = 5.90
3x = 1.50
x = 0.50
Each can of mushrooms is 50 cents, and the 3-bean salad is 88 cents
for each can.