Question

Two friends, Alejandro and Mia, agreed to split the check at a restaurant. Alejandro ordered $12 worth of food and Mia ordered $18 worth. At the end of the meal, Alejandro put his $12 contribution on the table, plus a $20% tip on his bill and Mia put her $18 contribution on the table, plus a $15% tip on her bill.

The total tip left by Alejandro and Mia is equal to r% of the total check for their table, where the "total check" amount does not include the tip. What is r?

Answer 1

17

Explanation:

Alejandro tipped 20% of $12, which is (0.2) ∙ $12 = $2.40.

Mia tipped 15% of $18, which is (0.15) ∙ $18 = $2.70.

Thus, the total tip they left was $2.40 + $2.70 = $5.10. We want to know what percent of $30 this is, so we set

5.10 = r% ∙ 30

= r\100 ∙ 30.

Multiplying both sides by 100 gives

510 = r ∙ 30.

The solution is r = 17 (in other words, Alejandro and Mia's total tip is equal to 17% of the total check).

Answer 2

Cost of Alejandro's food = $12

Tip paid by Alejandro = 20% of his bill = 20% of 12 = 2.4

Cost of Mia's food = $18

Tip paid by Mia = 15% of his bill = 15% of 18 = 2.7

Total Tip Paid = 2.4+2.7 = 5.1

Total Check Amount = 12 + 18 = 30

Total tip paid by Alejandro and Mia is r% of the total check amount.

So, we need to determine what % of 30 is equal to 5.1%

⇒ r% × 30 = 5.1

⇒ r% = 5.1 / 30

⇒ r% = 17%

Hence, r is 17%