# In a Spring Sale, a bag of springs now costs £3.60. What was it worth before the 20% sale?

May 4, 2017

See the entire solution process below:

#### Explanation:

The formula for determining the final cost of an item on sale is:

$c = p - \left(d \cdot p\right)$

Where:

$c$ is the final cost - £3.60 for this problem.

$p$ is the original price of the item - what we are solving for in this problem.

$d$ is the discount rate - 20% for this problem. "Percent" or "%" means "out of 100" or "per 100", Therefore 20% can be written as $\frac{20}{100}$.

Substituting and solving for $p$ gives:

£3.60 = p - (20/100 * p)

£3.60 = (100/100 * p) - 20/100p

£3.60 = 100/100p - 20/100p

£3.60 = (100 - 20)/100p

£3.60 = 80/100p

color(red)(100)/color(blue)(80) * £3.60 = color(red)(100)/color(blue)(80) *80/100p

(£360)/color(blue)(80) = cancel(color(red)(100))/cancel(color(blue)(80)) * color(blue)(cancel(color(black)(80)))/color(red)(cancel(color(black)(100)))p

£4.50 = p

Before the sale the bag of springs was worth £4.50