Question

One number is four times the other number. If 6 is added to the smaller number and 4 is added to the larger number, then the later number becomes twice the other number. Find the numbers .

Answer 1

Let the first(smaller) number = x

Let the other(larger) number= y

One number is four times the other number.

• y=4x

If 6 is added to the smaller number, we have: x+6

If 4 is added to the larger number, we have: y+4

Then the later number becomes twice the other number

• The later number = y+4

Therefore:

y+4=2(x+6)

`\begin{gathered} y+4=2\left(x+6\right) \\ \text{Recall: y=4x} \\ \text{Therefore we have:} \\ 4x+4=2(x+6) \\ 4x+4=2x+12 \\ 4x-2x=12-4 \\ 2x=8 \\ \text{Divide both sides by 2} \\ x=4 \end{gathered}`

Next, we substitute x=4 to find the value of y

`\begin{gathered} y=4x \\ y=4*4 \\ y=16 \end{gathered}`

The numbers are 4 and 16.