Question

8) Eugene wrote a riddle: A positive number is 5 less than another positive number. Six times the lesser number minus 3 times the greater number is 3. Find the two positive numbers.

Answer 1

Answer: the two numbers are 6 and 11.

Set up the individual equation according to the verbal statements:

A positive number is 5 less than another positive number:

a = b - 5       (this also implies that a<b)

Six times the lesser number minus 3 times the greater number is 3.

$6 a -3 b = 3$

Find the two positive numbers.

This is a system of linear equations - solve for a and b:

$6(b-5)-3b=6b-30-3b=3b-30=3\\3b=33\\b=11\\\rightarrow a=11-5 = 6$