Question

One number is less than a second number. The first is more than times the second. Find the numbers. Be sure to show all work on your paper. The answer without work will receive zero credit.

Answer 1

Question: One number is one less than a second number. Twice the first is 4 more than 5 times the second. Find the numbers.

Answer:

The numbers are -3 and -2

Explanation:

Given

Let the numbers be a and b

From the first statement:

`a = b - 1`

From the second:

`2a = 4 + 5b`

Required

Find a and b

Substitute b - 1 for a in the second equation

`2(b-1) = 4 + 5b`

`2b-2 = 4 + 5b`

Collect like terms

`2b- 5b = 2+ 4`

`-3b = 6`

`b =-2`

Recall that:

`a = b - 1`

`a = -2 - 1`

`a =- 3`