Question

Corn costs 99 cents per pound, and beans cost 45 cents per pound. If Shea buys 24 total pounds of corn and beans, and it costs $\$18.09$, how many pounds of corn did Shea buy? Express your answer as a decimal to the nearest tenth.

Answer 1

Shea bought 13.5 pounds of corn

c = pounds of corn
b = pounds of beans

Here’s what we know:
c(0.99) + b(0.45) = 18.09
c + b = 24

Solve the second equation for c in terms of b

c = 24-b

Substitute that expression for c in our first equation to get a numerical solution for b:

0.99 (24-b) + 0.45b = 18.09
23.76 - 0.99b + 0.45b = 18.09
-0.54b = -5.67
b = 10.5

Substitute that value to get a numerical value for c:

c = 24 - b
c = 24 - 10.5
c = 13.5

Check the math:

0.99(13.5) + 0.45(10.5) =
13.365 + 4.725 = 18.09