Happy Space toy store bought \(50\) plush toy otters for \(\$8.00\) each for resale. They also paid a \(\$30\) shipping fee.
They priced the toy otters at \(\$10.00\) each throughout December, after which they sold the remainder at a reduced sale price.
If they sold \(30\) toy otters in December for \(\$10.00\) each, what must the reduced sale price per otter be in order that they break even on this item (that is, they have no net profit nor loss)?
For each otter, what percentage of the \(\$10.00\) price is the savings from the reduced price?
To break even, Happy Space must recover their total cost for the otters, which is \((\$8.00\times 50) + \$30.00=\$430.00\).
The income from the sale of \(30\) otters at \(\$10\) each is \(30\times\$10.00=\$300\).
Thus, they need to recover \(\$430-\$300=\$130\) from the sale of the remaining \(20\) otters at a reduced price in order to break even.
This requires that the otters be priced at \(\$130\div 20=\$6.50\). So the appropriate reduced sale price is \(\$6.50\) to break even.
The reduced sale price of \(\$6.50\) is \(\$10.00-\$6.50=\$3.50\) less than the original price. Thus, as a percentage, this savings is \[\frac{\$3.50}{\$10.00}\times 100\%=0.35\times 100\%=35\%\]