Mr. Carey paid $12 for 2 large popcorns and 2 large drinks that his family will share. Mrs. Molina bought 1 large popcorn and 4 large drinks and paid $15. How much does each item cost?

Answer 1

Hi, Jennifer,

Let P and D stand for the price of individual popcorn and large drink purchases. We can take what the problem says and make some equations. We can state that the total cost for both Carey and Molina are the sum of the cost of both categories, Popcorn and Drinks. We just multiply the number they bought times the cost per item, P and D:

Carey: 2P + +2D = 12

Molina: 1P + 4D = 15

Pick one of the two equations and rearrange it to find an expression of either P or D. I'll chose the second (Molina) and rearrange it to tell us what P is equal to:

P = 15 - 4D

Now use that in the other equation by substitution:

2(15-4D)+2D=12

30-8D+2D=12

-6D = -18

D = 3

Now use D = 3 in either equation to find the value of P:

P = 15 - 4D

P = 15 - 4(3)

P = 3 (!)

They are the same price, according to our numbers. Try these values, just to be sure.

Carey: 2P + +2D = 12 ??

2*3 + 2*3 = 12 Yes

Molina: 1P + 4D = 15 ??

1*3 + 4*3 =15 Yes

That was fun. I hope it helps,

Bob

Answer 2

2p + 2d = 12

1p + 4d = 15

Can you eliminate either p or d and answer?