$20$ If you buy a new sweatshirt that is priced at $\$ 35$ , and pay $37$ . $50$ after tax, what was the sales tax rate? Round to the nearest whole percent.

Full solution

20

If you buy a new sweatshirt that is priced at

\$ 35

, and pay

37

50

after tax, what was the sales tax rate? Round to the nearest whole percent.

Identify Costs: Identify the total cost, the original price, and the amount paid in tax. $\newline$ The original price of the sweatshirt is $\$35$ , and the total cost after tax is $\$37.50$ . To find the amount paid in tax, subtract the original price from the total cost. $\newline$ Amount paid in tax = Total cost after tax - Original price $\newline$ Amount paid in tax = $\$37.50 - \$35$ $\newline$ Amount paid in tax = $\$2.50$
Calculate Tax Rate: Calculate the sales tax rate as a decimal. $\newline$ To find the sales tax rate, divide the amount paid in tax by the original price. $\newline$ Sales tax rate (as a decimal) = Amount paid in tax / Original price $\newline$ Sales tax rate (as a decimal) = $\$2.50 / \$35$ $\newline$ Sales tax rate (as a decimal) = $0.07142857142857142$
Convert to Percentage: Convert the sales tax rate from a decimal to a percentage and round to the nearest whole percent. $\newline$ To convert the decimal to a percentage, multiply by $100$ and round to the nearest whole number. $\newline$ Sales tax rate (as a percentage) = Sales tax rate (as a decimal) $\times 100$ $\newline$ Sales tax rate (as a percentage) = $0.07142857142857142 \times 100$ $\newline$ Sales tax rate (as a percentage) $\approx 7.14\%$ $\newline$ Rounded to the nearest whole percent, the sales tax rate is approximately $7\%$ .