Question

The sum of three numbers is 69. If the second number is equal to the first diminished by 8, and the third number is 5 times the first. What are the numbers?The sum of three numbers is 69. If the second number is equal to the first diminished by 8, and the third number is 5 times the first. What are the numbers?The sum of three numbers is 69. If the second number is equal to the first diminished by 8, and the third number is 5 times the first. What are the numbers?

Answer 1

They are 3, 11 and 55.

Explanation:

x +y + z = 69

y = x - 8

z = 5x

Substitute z = 5x in the first equation:

x + y + 5x = 69

6x + y = 69.........(1)

From the second equation

-x + y = -8.........(2)

Subtract equations (1) - (2):

7x = 77

x = 11

So z = 5x = 5*11 = 55 and

y = x - 8 = 11 - 8 = 3..

Answer 2

x = 11, y = 3 and z = 55

Explanation:

Let the three numbers be x, y and z. Then x + y + z = 69

Then y = x - 8, and z = 5x. Substituting these expressions in x into

x + y + z = 69, we get: x + x - 8 + 5x = 69, or

7x = 77, so that x = 11.

If x = 11, then:

y = x - 8 = 11 - 8 = 3, and:

z = 5x = 5(11) = 55

Then x = 11, y = 3 and z = 55.

Check: Do these three numbers add up to 69? 11 + 3 + 55 = 69? YES