Question

There are four numbers. The average of the first three is 15, and of the last three is 16. If the last number is 19, find the first number.

A. 16
B. 14
C. 12
D. 10

Answer 1

To find the first number given the averages of different sets and the value of the last number, use arithmetic to create equations and solve for the unknown. The first number is found to be 16.

Step-by-step explanation:

The student asked to find the first number given that the average of the first three numbers is 15, the average of the last three numbers is 16, and the last number is 19. To solve this, first, let's denote the four numbers as A, B, C, and D, where D is the last number that we know is 19. We can create two equations based on the information given:

• (A+B+C)/3 = 15
• (B+C+D)/3 = 16

By multiplying both equations by 3 to eliminate the fraction, we get:

• A+B+C = 45
• B+C+19 = 48

We can now subtract the first equation from the second to find the value of A:

• (B+C+19) - (A+B+C) = 48 - 45
• 19 - A = 3
• A = 16

Therefore, the first number is 16, which corresponds to option A.