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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
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Sep 28, 2022
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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.
Mathematics
high-school
Nadiya
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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
Spike Gronim
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Oct 5, 2022
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Spike Gronim
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