Martha picked out a pair of shoes she wanted to buy. The cashier told her that the shoes were on sale for 30% off the original price. She rang up the sale price plus 5% tax, so Martha ended up paying $58.80 for her shoes. What was the original price for the shoes?

- I am only confused about why the 5% tax added is simplified to 1.05. Why is 1 added to it?

Question

Martha picked out a pair of shoes she wanted to buy. The cashier told her that the shoes were on sale for 30% off the original price. She rang up the sale price plus 5% tax, so Martha ended up paying $58.80 for her shoes. What was the original price for the shoes?

- I am only confused about why the 5% tax added is simplified to 1.05. Why is 1 added to it?

inkyvoyd · Answer

Because, you multiply the tax by 105%. A 5% tax means the total price is 105% of the original (a 5% increase), not 5% of the orignial (which is much less than the orignial)

anonymous · Answer

Thank you. Also, why am I supposed to multiply 1.05(0.7x) and not add it up like 1.05+0.7x?

anonymous · Answer

100% <-  original price
5% <- tax
100% + 5% = 105%  <- original price + tax

anonymous · Answer

Thank you. Also, why am I supposed to multiply 1.05(0.7x) and not add it up like 1.05+0.7x?

anonymous · Answer

$$
y = x-(30\%)x = (100\%-30\%)x = (70\%)x \
$58.80 = y + (5\%)y = (100\%+5\%)y = (105\%)y = (105\%)(70\%)x
$$

anonymous · Answer

In this case $y$ is pre-tax and $x$ is pre-sale.