Algebra Word Problem

Question

The sum of two numbers is 46. One third of their difference is 10. What are the 2 numbers?

Answer 1

Hello, William

Let's call the numbers, X and Y

X + Y = 46

1/3 of their difference is 10.

1/3(X - Y) = 10

Okay, so let's solve the first equation for one unknown

X + Y - Y = 46 - Y

X = 46 - Y

Now, we can substitute for X in the 2nd equation:

1/3((46 - Y) - Y ) = 10

Now, multiply both sides by 3 to get rid of the fraction

46 - 2Y = 30

46 - 2Y + 2Y = 30 + 2Y

46 - 30 = 30 + 2Y - 30

16 = 2Y

Y = 8

Since X + Y = 46, then X + 8 = 46

so X = 38

Now, check the 2nd equation:

1/3(X - Y ) = 10

1/3(38 - 8) = 1/3(30) = 10

Yes, the answers are correct.

X = 38

Y = 8