Question

Andrea went to the store to buy a sweater that was on sale for 40% off the original price. it was then put on clearance at an additional 25% off the sale price. she also used a coupon that saved her an additional $5. andrea did not spend more than $7.60 for the sweater. What are the possible values for the original price of the sweater?

Answer 1

Explanation:

x ≤ $28

Answer 2

Here, we want to calculate the possible values for the original price of the sweater.

Let the original price of the sweater be $x

We are told that the sales price is 40% off the original price

Mathematically, we can calculate the discount as follows;

40/100 * x = 0.4x

Now, the sales price is Original price - discount

So, the sales price will be x - 0.4x = 0.6x

Furthermore, there was a clearance at an additional 25%

The discount from the clearance sales will be

25/100 * sales price

25/100 * 0.6x

0.25 * 0.6x = 0.15x

So the clearance price will be

0.6x - 0.15x = 0.45x

Now, she used a coupon that saved her $5

So, the amount to be paid will be;

0.45x - 5

Also, we are told that Andrea did not spend more than $7.60

This means we have an inequality that can be defined as the amount to be paid is no more than $7.60

Representing this, we have;

`0.45x\text{ - 5 }\leq\text{ 7.60}`

We now proceed to solve this inequality;

0.45x ≤ 7.60 + 5

0.45x ≤ 12.6

x ≤ 12.6/0.45

x ≤ $28

So the possible values for the original price of the sweater are values which are less than or equal to $28

Examples of these include 27,26,25,24 upto $1 , since the price paid cannot be negative