Question

A number, y, is equal to the difference of a larger number and 3. The same number is one-third of the sum of the large number and 9. Which equations represent the situation?

Answer 1

Let the larger number be x.

A number, y, is equal to the difference of a larger number and 3.

y = x - 3

x - y = 3

The same number is one-third of the sum of the large number and 9.

y = (1/3)(x + 9)

3y = x + 9

x - 3y = -9

The equations are:
x - y = 3
x - 3y = -9

Answer 2

The equation represents the situation are as follows;

$\rm x -y=3$

$\rm x -3y =-9$.

Given that

A number, y, is equal to the difference of a larger number and 3.

The same number is one-third of the sum of the large number and 9.

We have to determine

Which equations represent the situation?

According to the question

Let the number be y,

And the larger number be x.

A number, y, is equal to the difference of a larger number and 3.

$\rm y = x-3\\\\x -y=3$

And the same number is one-third of the sum of the large number and 9.

$\rm y = \dfrac{1}{3} (x+9)\\\\3y = x+9\\\\ x -3y =-9$

Hence, the equation represents the situation are  $\rm x -y=3$ and $\rm x -3y =-9$.

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