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MAT-144 · In-person sections Exam 1 Review · Unit 1
Exam 1 Review · Q5

Finding the original price given the sale price and percent

You are told the sale price IS some percent of the original. One division recovers the original — the only trap is dividing by the wrong number.

01 Worked Example Video

Every step of Finding the original price given the sale price and percent explained on video. Pause anywhere; the embed scrolls independently of the page.

YOUTUBE
02 What This Looks Like on ALEKS

ALEKS randomizes the numbers each attempt, but the question shape stays the same. Here are three example versions you might see.

A table

A table is on sale for $456. This is 76% of its regular price.

What is the regular price? Type just the number.

$
An awkward number

A lamp is selling for $145.60, which is 91% of its regular price.

What is the regular price? Type just the number.

$
Not a discount

After a tip, a restaurant bill came to $92. That is 115% of the food total.

What was the food total? Type just the number.

$
Heads up: Your ALEKS version will use different numbers. The numbers in the practice below are different too — that way you're exercising the move, not memorizing one answer.
03 The Rule
original = sale price ÷ the percent as a decimal, not as a whole number
the answer is always bigger than the sale price you are undoing a discount, not applying one
“$207 is 69% of the regular price” says 0.69 × regular = 207. Divide both sides by 0.69 and the regular price falls out. Note that the percentage here is handed to you — unlike the sister question, where you are given the size of the discount and have to work out what fraction is left.
Common slips
(1) Multiplied instead of dividing. That applies the discount again and gives a smaller number. The original must be bigger. (2) Subtracted the percent first. The question already tells you the sale price is 69% of the original; do not turn it into 31%. (3) Divided by 69 rather than 0.69. That answer is a hundred times too small.
04 Practice — Step by Step
One division, one check

Today only, a coat is being sold for $207. This is 69% of its regular price.

What was the price yesterday?

Step 1

Which way does it go?

You are recovering the regular price from the sale price. Do you multiply or divide by 0.69?
Step 2

Do it

207 ÷ 0.69. What was the regular price?
$
Step 3

Check it forwards

Confirm by going the other way: what is 69% of $300?
$
▸ Related Mini Lessons
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MAT-144 · EXAM 1 REVIEW · Q5 OF 20