Question

Six times a larger number is equal to the sum of a smaller number and 18. The difference of twice the larger number and the

Answer 1

The set of equations that represent this situation is:

$y = \frac{1}{6}x + 3$

$y = \frac{1}{2}x + 3$

Solution:

Let "x" represent the smaller number

Let "y" represent the larger number

Given that,

Six times a larger number is equal to the sum of a smaller number and 18

Here "times" represents multiplication

Six times a larger number = sum of a smaller number and 18

6 x larger number = smaller number + 18

6y = x + 18

Thus,

$y = \frac{1}{6}(x + 18)\\\\y = \frac{1}{6}x + 3$

Also given that difference of twice the larger number and the  smaller number is 6

twice the larger number - smaller number = 6

2y - x = 6

Thus,

2y = x + 6

$y = \frac{1}{2}(x + 6)\\\\y = \frac{1}{2}x + 3$

Thus the set of equations that represent this situation is:

$y = \frac{1}{6}x + 3$

$y = \frac{1}{2}x + 3$