Question

Sylvia is going to pick out a souvenir hat while she is on vacation. She knows the price of the hat will ___ by 5% when she pays sales tax.

She writes the ___ h+0.05h to find the ___ she will pay for the hat if it costs h dollars. Jin correctly writes another expression, 1.05h, that will also find the the ___ Sylvia will pay for the hat if it ___ h dollars.
Use the drop-down menus to explain what each part of Sylvia's and Jin's expressions mean.

Answer 1

Sylvia's expression h+0.05h and Jin's expression 1.05h both calculate the final price of a hat including a 5% sales tax. Jin's method is more concise and shows the total price as a single multiplication.

Step-by-step explanation:

Sylvia is calculating the total cost of a hat with a 5% sales tax. Her expression h+0.05h represents the original price of the hat (h) plus 5% of that price as sales tax (0.05h). The term 0.05h is found by converting 5% to a decimal and multiplying it by the hat's price.

Jin's expression, 1.05h, simplifies the calculation by combining the original price and the tax into one multiplicative factor, where 1 represents 100% of the original price, and 0.05 represents the 5% sales tax. This results in the same final cost as Sylvia's expression but in a more concise form. To find the total price a customer would pay, either expression can be used to add the appropriate sales tax to the original price.