Question

The larger of two numbers is 7 times the smaller number. Three times the larger number is 7 more than 4 times the smaller number. Find the numbers.

Answer 1

Let the smaller number be x.

Smaller number = x
Larger number = 7x

3 times the larger number is 7 more than 4 times the smaller number:
3(7x) = 4x + 7
21x - 4x = 7
17x = 7
x = 7/17
7x = 49/17

Smaller number = 7/17
Larger number = 49/17

Answer 2

Let x represent the smaller number.
.. 3(7x) = 7 +4x
.. 21x = 7 +4x
.. 17x = 7
.. x = 7/17

The smaller number is 7/17. The larger number is 7*7/17 = 2 15/17.