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Levi had a coupon for 30% on his favorite clothing store. He uses it to buy a shirt and a pair of shorts.

(A) Levi payed $36 for the shorts after using the coupon. What was the regular price of the shorts?

(B) The normal price of the shirt is $22. What did Levi pay for the shirt?

(C) If the regular price of an item is p dollars, what is the discount price in dollars?

1 Answer

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Answer:

(A) $51.43

(B) $15.40

(C) d = 0.70p, or d = (1 -r)p for discount rate r

Explanation:

Given Levi used a 30% off coupon for his clothing, you want to know the regular price if Levi paid $36, the sale price if the regular price is $22, and the discount price for an item with a regular price of p.

(C) Discount price

We can work the problem for the general case, then use that solution for the specific cases given.

We know the relationship between the prices is ...

(discount price) = (regular price) - (discount rate) × (regular price)

Using ...

  • p = regular price
  • r = discount rate
  • d = discount price

we can write the same equation using these letters:

d = p - r·p

d = p(1 -r) . . . . . . . equation for part B

Solving for p, we have an equation we can use for part A

p = d/(1 -r) . . . . . . divide by the coefficient of p

The discount price (d) when an item of regular price p is discounted by rate r is d = p(1 -r). d = 0.70p when r = 30%.

(A) Regular price

p = d/(1 -r) = $36/(1 -0.30) ≈ $51.43

The regular price of the shorts was $51.43.

(B) Discount price

d = p(1 -r) = $22(1 -0.30) = $15.40

Levi paid $15.40 for the shirt.

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Additional comment

Algebra teaches us that we can manipulate symbols using the same operations we use to manipulate numbers. Given specific examples of relations between regular price, discount rate, and discount price (parts A and B), the only thing you need to do to work the generic problem of part C is assign variable names to the quantities involved and make use of the same relations you used already.

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Levi had a coupon for 30% on his favorite clothing store. He uses it to buy a shirt-example-1
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