Tax and tip word problems

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Problem

Neal buys a board game. He pays for the board game and pays $\$1.54$dollar sign, 1, point, 54 in sales tax. The sales tax rate is $5.5\%$5, point, 5, percent.

What is the original price of the board game, before tax?

$\$\$dollar sign, space

Hint #11 / 5

To find the original price, first we need to answer, $\$\greenD{1.54}$dollar sign, start color #1fab54, 1, point, 54, end color #1fab54 is $\blueD{5.5}\%$start color #11accd, 5, point, 5, end color #11accd, percent of what number?

Hint #22 / 5

Percent means per hundred, so $\blueD{5.5}\%$start color #11accd, 5, point, 5, end color #11accd, percent is equivalent to $\blueD{\dfrac{5.5}{100}}$start color #11accd, start fraction, 5, point, 5, divided by, 100, end fraction, end color #11accd which is also equal to $\blueD{5.5\div 100}$start color #11accd, 5, point, 5, divided by, 100, end color #11accd.

$\blueD{5.5 \div 100 = 0.055}$start color #11accd, 5, point, 5, divided by, 100, equals, 0, point, 055, end color #11accd

Hint #33 / 5

To find the original price, we need to know $\blueD{0.055}$start color #11accd, 0, point, 055, end color #11accd times what number equals $\greenD{1.54}$start color #1fab54, 1, point, 54, end color #1fab54.

$\blueD{0.055} \maroonD{x} = \greenD{\$1.54}$start color #11accd, 0, point, 055, end color #11accd, start color #ca337c, x, end color #ca337c, equals, start color #1fab54, dollar sign, 1, point, 54, end color #1fab54

Hint #44 / 5

$\begin{aligned} \blueD{0.055} \maroonD{x} &= \greenD{\$1.54} \\\\ \dfrac{\blueD{0.055} \maroonD{x}}{\blueD{0.055}} &= \dfrac{\greenD{\$1.54}}{\blueD{0.055}} \\\\ \maroonD{x} &= \maroonD{28} \end{aligned}$

Hint #55 / 5

The original price of the board game is $\$\maroonD{28}$dollar sign, start color #ca337c, 28, end color #ca337c.