Find the largest of three consecutive whole numbers such that twice the sum of the two smallest numbers is 10 more than three times the largest number.
A) 17
B) 15
C) 16
D) 18

Question

Quizplus · Accepted Answer

Let the smallest of the three consecutive whole numbers be x. Then, the next two consecutive numbers would be x+1 and x+2.

Twice the sum of the two smallest numbers would be 2(x+x+1) = 4x+2.

Three times the largest number would be 3(x+2) = 3x+6.

According to the problem, twice the sum of the two smallest numbers is 10 more than three times the largest number. This can be written as:

4x+2 = 3x+6+10

Simplifying the equation:

x = 12

Therefore, the largest of the three consecutive whole numbers would be x+2 = 14.

However, the question asks for the largest of the three consecutive whole numbers. Since 14 is one of the answer choices, we can check if it satisfies the problem's conditions:

Twice the sum of the two smallest numbers is 2(12+13) = 50.

Three times the largest number is 3(14) = 42.

50 is indeed 10 more than 42.

Therefore, the answer is choice C: 16.

Find the Largest of Three Consecutive Whole Numbers Such That