A customer at a restaurant leaves $80 on the table to pay for the food, a 15% tip, and 8% sales tax. If both tip and sales tax w

Question

Phantasy

1 month ago

12

A customer at a restaurant leaves $80 on the table to pay for the food, a 15% tip, and 8% sales tax. If both tip and sales tax w

ere calculated from
the cost of the food, which of the following was the cost of the food, rounded to the nearest cent?

Mathematics

1 answer:

zzz [12.3K] · Answer 1 · 2026-04-11T19:34:11+03:00

Answer:

$65.04

Step-by-step explanation:

Given:

Total amount left by the customer on table = $80

This includes the cost of food, 15% tip, and 8% sales tax.

Both sales tax and tip are based on the cost of the food.

To find:

Cost of the food =?

Solution:

Let's denote the cost of food as $ $x$

According to the problem statement:

Tip = 15% of $x$

Sales Tax = 8% of $x$

Amount remaining on the table = Cost of food + Tip + Sales tax

$80 = $x$ + 15% of $x$ + 8% of $x$

Now, let’s resolve the equation:

$\$80 = x + 15\%\ of\ x + 8\%\ of\ x\\\Rightarrow 80 = x + \dfrac{15}{100} \times x + \dfrac{8}{100} \times x\\\Rightarrow 80 = \dfrac{100x + 15\times x + 8\times x}{100}\\\Rightarrow 80 = \dfrac{123x}{100}\\\Rightarrow 80 \times 100= 123x\\\Rightarrow x = \dfrac{8000}{123}\\\Rightarrow \bold{x = \$65.04}$

Consequently, the cost of food, when rounded to the nearest cent, is $65.04.