# Work out the normal price in the second shop ?

## 2 shops are selling the same hoover. in the first shop the customer pays £7.25 per month for 13 months. in the second shop the customer gets 35% discount on the shops normal price. with these offers the customer pays the same amount in total for the hoover.

Jun 24, 2018

Normal price in the second shop is £146.54 to 2 decimal places.

#### Explanation:

Shop 1 ->13xx£7.25 = £94.25

Set the original price as $x$ and drop the £ sign

Shop 2 $\to x - \frac{35}{100} x = 94.25$

Lets look at Shop 2 another way.

If there was 35% discount then what was paid was 100%-35%=65%

So we have: $\frac{65}{100} x = 94.25$

Multiply both sides by .$\textcolor{red}{\frac{100}{65}}$

$\textcolor{g r e e n}{\frac{65}{100} x = 94.25 \textcolor{w h i t e}{\text{dddd")->color(white)("dddd}} \frac{65}{100} \textcolor{red}{\times \frac{100}{65}} \times x = 95.25 \textcolor{red}{\times \frac{100}{65}}}$

$x = 146.53846 \ldots$

x=£146.54 rounded to 2 decimal places
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$\textcolor{b l u e}{\text{Foot note}}$

Paying over a period usually costs more (interest). So perhaps the first shop would be a better buy if you paid in full. That way you do not pay interest.