Question

The sum of two numbers is 21.

The second number is six times the first number.
Work out the two numbers.

Answer 1

3 and 18.

Explanation:

If one number is x then the other is 6x.

So, x + 6x = 21

7x = 21

x = 3.

The other number is 21 - 3 = 18.

Answer 2

Pretend that x and y represents the 2 numbers that we need to find.

According to the information, we know that:

x + y = 21

6x = y

Replace y in the first equation with 6x (because they are equal to each other according to the second equation):

x + y = 21

x + 6x = 21

7x = 21

x = 21/7 = 3

Now have two ways to find y, both will give us the same result:

3 + y = 21 ⇔ y = 21 - 3 = 18

6 · 3 = y ⇔ y = 18

So the numbers that we need to find are 3 and 18.