I AM SUPPOSE TO FORM TWO DIFFERENT EQUATIONS OUT OF THIS WORD PROBLEM BUT I NEED HELP DOING THAT

Question

Gia is at the candy store and trying to figure out which coupon she should use. Candy costs $2.50 per pound plus an additional $0.75 charge for a candy bag. She can use a free coupon that will give her 30% off of just her candy purchase, or she can pay $5.00 for a coupon that will give her 50% off her purchase and a free candy bag.

Answer 1

Hi, Endora:

Here's how I would tackle this one.

Although the question doesn't explicitly ask, we can assume the girl wants to pay the least amount of money. So, we need mathematical expressions for each of her coupon options, then see which one costs less.

Suppose she buys X pounds of candy.

Coupon option A: Cost(A) = 2.5 (1 - 30%) X + 0.75 for the candy and a bag

= 2.5 (0.7) X + 0.75

= 1.75X + 0.75 . . . . . . . . . . . . . .eqn (1)

Coupon option B: Cost(B) = 2.50 (1 - 50%) X+ 5.00 for the candy plus the extra charge

= 2.50 (1/2) X+ 5.00

= 1.25X + 5.00 . . . . . . . . . . . . . eqn (2)

Option A is cheaper iff 1.75X +0.75 < 1.25X + 5,00

=> 0.50X < 4.25

=> X < 4.25 / 0.50

=> X < 8.50 pounds of candy

So, if she buys strictly less than 8.5 pounds of candy, option A is better

At exactly 8.5 pounds of candy, A and B cost the same

If she buys more than 8.5 pounds of candy, option B is better.

Presumably, the phrase, "two different equations", refers to equations (1) and (2) above.