Math

Question Carlos has two coupons for 59pants.CouponA:59 pants. Coupon A: 5 rebate. Coupon B: 15% off. Choose the coupon that gives the lower price. The price with the better coupon is $$ less than the other.

Studdy Solution

STEP 1

Assumptions
1. The original price of the pants is 59.<br/>2.CouponAoffersa59.<br />2. Coupon A offers a 5 rebate on the pants.
3. Coupon B offers a 15% discount on the pants.
4. We need to determine which coupon provides a lower price for the pants.
5. We need to calculate the difference in price between the two coupons.

STEP 2

First, we calculate the price of the pants using Coupon A by subtracting the rebate from the original price.
PriceA=OriginalpriceRebatePrice_{A} = Original\, price - Rebate

STEP 3

Now, plug in the values for the original price and the rebate to calculate the price with Coupon A.
PriceA=$59$5Price_{A} = \$59 - \$5

STEP 4

Calculate the price with Coupon A.
PriceA=$59$5=$54Price_{A} = \$59 - \$5 = \$54

STEP 5

Next, we calculate the price of the pants using Coupon B by applying the percentage discount to the original price.
PriceB=Originalprice×(1Discountrate)Price_{B} = Original\, price \times (1 - Discount\, rate)

STEP 6

Convert the percentage discount to a decimal value.
15%=0.1515\% = 0.15

STEP 7

Now, plug in the values for the original price and the discount rate to calculate the price with Coupon B.
PriceB=$59×(10.15)Price_{B} = \$59 \times (1 - 0.15)

STEP 8

Calculate the price with Coupon B.
PriceB=$59×(10.15)=$59×0.85=$50.15Price_{B} = \$59 \times (1 - 0.15) = \$59 \times 0.85 = \$50.15

STEP 9

Now that we have the prices with both coupons, we compare them to determine which coupon gives the lower price.
PriceA=$54Price_{A} = \$54 PriceB=$50.15Price_{B} = \$50.15

STEP 10

Since PriceB<PriceAPrice_{B} < Price_{A}, Coupon B gives the lower price.

STEP 11

To find the difference in price between the two coupons, we subtract the price with Coupon B from the price with Coupon A.
Difference=PriceAPriceBDifference = Price_{A} - Price_{B}

STEP 12

Plug in the values for PriceAPrice_{A} and PriceBPrice_{B} to calculate the difference.
Difference=$54$50.15Difference = \$54 - \$50.15

STEP 13

Calculate the difference in price.
Difference=$54$50.15=$3.85Difference = \$54 - \$50.15 = \$3.85
Coupon B gives the lower price. The price with coupon BB is $3.85\$3.85 less than the price with coupon AA.

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