Question

A positive number is 5 less than 3 times another. The sum of the smaller number and 4 times the larger is 97. Find the smaller number

Answer 1

9

Explanation:

The first sentence of the problem can be interpreted two ways. The way that makes the second sentence work out correctly is ...

'a larger number is 5 less than 3 times a smaller number'

Using x for the smaller number, the two equations that can be written are ...

• 3x -y = 5
• x +4y = 97

Adding 4 times the first equation to the second, we get ...

4(3x -y) + (x +4y) = 4(5) +(97)

13x = 117 . . . . . simplify

x = 9 . . . . . . . . divide by 13

The smaller number is 9.