Question

NO LINKS!!

A couple does not wish to spend more than $100 for dinner at a restaurant. If a sales tax of 5% is added to the bill and they plan to tip 15% after the tax has been added, what is the most they can spend for the meal? (Round your answer to the nearest cent).

$____________

Answer 1

The most the couple can spend for the meal is $82.82 to the nearest cent.

Explanation:

Let x be the greatest amount (in dollars) that the couple can spend for the meal.

If a sales tax of 5% is added to the bill, then the bill will be:

`x+0.05x=1.05x`

If a tip of 15% is then added to the bill, the bill will be:

`1.05x+0.15 \cdot 1.05x=1.2075x`

If the maximum the couple can spend is $100 then:

`1.2075x\geq100`

Solve the equation for x:

`\begin{aligned}1.2075x &\geq 100\\\\x&\geq (100)/(1.2075)\\\\x&\geq 82.8157349...\end{aligned}`

Therefore, the most the couple can spend for the meal is $82.82 to the nearest cent.