Question

Shelly is going shopping at the mall to buy 3 pairs of shoes. She has a coupon for $2 off per pair of shoes after buying the first pair at full price. Shelly is willing to spend $80 to $176 not including tax. If the shoes she purchases are all the same price, what is the least and most amount she can spend per pair?

Answer 1

The least and most amount she can spend per pair is described in two cases given below.

Explanation:

Given Shelly is going shopping at the mall to buy 3 pairs of shoes. She has a coupon for $2 off per pair of shoes after buying the first pair at full price. Shelly is willing to spend $80 to $176 not including tax. If the shoes she purchases are all the same price.

we have to find the least and most amount she can spend per pair.

There are two cases which are to be considered one in which no coupon applied which gives minimum amount and the other in which coupon applied gives maximum amount.

Case 1 : Coupon not applied.

Let the cost of a pair of shoes is x

∴ the cost of 3 pair of shoes is 3x

hence, the amount of money she spend is 86<3x<176

⇒
`(86)/(3)<x<(176)/(3)`

⇒ 26.6<x<58.6

Case 2 : Coupon applied

Let the cost of a pair of shoes is x. Since, there is $2 off per pair of shoes after buying the first pair at full price.

∴ the cost of 3 pair of shoes after applying coupon is 3x-4

hence, the amount of money she spend is 86<3x-4<176

⇒
`(90)/(3)<x<(180)/(3)`

⇒ 30<x<60

These are the least and most amount she can spend per pair.

Answer 2

Answer: The answer is $24 and $60.

Step-by-step explanation: Given that Shelly is going to a shopping mall to buy 3 pair of shoes and she has a coupon of $2 off per pair of shoes if she she buy one pair at the full price. Shelly can spend between $80 to $176.

WE need to find the least and most amount she can spend per pair if she purchases all the three pairs at the same price.

Let, Shelly spent $x on the first pair she purchased. Then, she will be getting the rest two pair of shoes each at a price of $(x-2).

Therefore,

`80\leq x+(x-2)+(x-2)\leq 176\\\\\Rightarrow 80\leq 3x-4\leq 176\\\\\Rightarrow 84\leq 3x\leq 180\\\\\Rightarrow 28\leq x\leq 60.`

Thus, she can spend at least $28 and at most $60 per pair of shoes.