Math  /  Numbers & Operations

QuestionTrey has two coupons for a phone. Coupon A: $45\$ 45 rebate on a $65\$ 65 phone Coupon B: 65%65 \% off of a $65\$ 65 phone Choose the coupon that gives the lower price. Then fill in the blank with the correct value. Coupon A gives the lower price. The price with coupon A is S \square less than the price with coupon B. Coupon B gives the lower price. The price with coupon B is $\$ \square less than the price with coupon A.

Studdy Solution

STEP 1

1. Coupon A provides a flat \$45 rebate on a \$65 phone.
2. Coupon B provides a 65% discount on a \$65 phone.
3. We need to determine which coupon results in a lower price and calculate the difference between the two prices.

STEP 2

1. Calculate the price using Coupon A.
2. Calculate the price using Coupon B.
3. Compare the prices and determine the lower price.
4. Calculate the difference between the two prices.

STEP 3

Calculate the price of the phone after applying Coupon A.
Original price of the phone = \$65
Rebate from Coupon A = \$45
Price with Coupon A = Original price - Rebate
\[ \text{Price with Coupon A} = 65 - 45 = 20 $

STEP 4

Calculate the price of the phone after applying Coupon B.
Discount percentage from Coupon B = 65%
Price with Coupon B = Original price ×\times (1 - Discount percentage)
\[ \text{Price with Coupon B} = 65 \times (1 - 0.65) = 65 \times 0.35 = 22.75 $

STEP 5

Compare the prices obtained from Coupon A and Coupon B.
Price with Coupon A = \$20
Price with Coupon B = \$22.75
Since \$20 < \$22.75, Coupon A gives the lower price.

STEP 6

Calculate the difference between the two prices.
Difference = Price with Coupon B - Price with Coupon A
\[ \text{Difference} = 22.75 - 20 = 2.75 $
Coupon A gives the lower price. The price with Coupon A is \$2.75 less than the price with Coupon B.

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