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 [tex]\$18.09[/tex], how many pounds of corn did Shea buy? Express your answer as a decimal to the nearest tenth.

To determine the pounds of corn Shea bought, we solve the system of equations from the pricing and amount information. We establish two equations based on the prices per pound and total pounds purchased and costs, then solve for the quantity of corn. Shea bought approximately 13.5 pounds of corn.

Explanation:

To solve how many pounds of corn Shea bought, we need to set up a system of equations. Let's define C as the pounds of corn Shea bought and B as the pounds of beans. Given that corn costs $0.99 per pound and beans cost $0.45 per pound, the first equation can be represented as:

C + B = 24 (1)

The total cost of the corn and beans is $18.09, so the second equation based on the cost is:

0.99C + 0.45B = 18.09 (2)

We can solve this system of equations using substitution or elimination. Let's use substitution. We solve equation (1) for B:

B = 24 - C

Now, we substitute B in equation (2):

0.99C + 0.45(24 - C) = 18.09

If we solve for C, we get:

0.99C + 10.8 - 0.45C = 18.09

C(0.99 - 0.45) = 18.09 - 10.8

C(0.54) = 7.29

C = 7.29 / 0.54

C ≈ 13.5

Therefore, Shea bought approximately 13.5 pounds of corn.