Question

Charles is in charge of cooking broccoli and zucchini for a large group. He has to spend all $20.10 he has and can carry 11 pounds of veggies. Zucchini costs $1.60 per pound and broccoli costs $2.10 per pound. How many pounds each of zucchini and broccoli can Charles get so that he spends all $20.10 and gets 11 pounds of veggies? Let x represent the number of pounds of zucchini and y represent the number of pounds of broccoli. Show ALL work!

Answer 1

Total equation: X + Y = 11 pounds

Cost equation: 1.60X + 2.10Y = 20.10

Number of Pounds of Zucchini = 6

Number of Pounds of Broccoli = 5

Explanation:

You get the equations by just pulling the information from the text.

We then take the total equation and rearrange it to solve for one of our values. I will be using X

X + Y = 11 so first subtract X from both sides to get

Y = 11 - X so now we know what Y equals

next take the cost equation and input X in wherever it shows up so

1.60 (X) + 2.10 (11 - X) = 20.10

now distribute 2.10 to the values in the parathesis to get

1.60X + 23.1 - 2.10X = 20.10

now combine like terms

-0.5X + 23.1 = 20.10

now subtract 23.1 from both sides

-0.5X = -3

now divide both sides by -0.5

X = 6

so now we know that he both 6 pounds of zucchini now plug that into the total equation

6 + Y = 11

subtract 6 from both sides

Y = 5