One number is 2/3 of another number. The sum of the two numbers is 10. How do you find the two numbers?

2 Answers
Oct 26, 2016

The two numbers are 4 and 6.

Explanation:

Let one number be represented as x and the other as y.

According to the problem:

x=2/3y and x+y=10

From the second equation we get:

x+y=10

:.color(red)(y=10-x) (subtracting x from both sides)

Replacing the value of y in the first equation we get:

x=2/3color(red)(y)

x=2/3color(red)((10-x))

Multiplying both sides by 3 we get:

3x=2(10-x)

Opening the brackets and simplifying we get:

3x=20-2x

Add 2x to both sides.

5x=20

Divide both sides by 5.

x=4

Since from the second equation we have:

x+y=10

substituting x with 4 we get:

4+y=10

Subtract 4 from both sides.

y=6

Oct 26, 2016

The numbers are 4 and 6.

Explanation:

This question can also be done by using just one variable.
Define each variable and then form an equation.

Let the larger number be x.
The other number is 2/3x

The sum of the numbers is 10.

x+2/3x = 10" "larr multiply by 3

3x + (3xx2x)/3 = 30

3x + 2x = 30

5x = 30

x = 30/5= 6" "larrthis is the larger number

2/3 (6) = 4" "larr this is the smaller number.

The numbers are 4 and 6.