The sum of two numbers is 60. The larger number is twice the smaller number. Find the numbers.

Answer 1

Since one number is described in terms of the other number, we can use a single variable here to represent both of the unknown numbers. Here's how: we'll let x = the smaller number. Then, because the larger number is described as "twice the smaller", we will let 2x represent the larger number.

The problem says the sum is 60, so now we will take both numbers, expressed in terms of our variable, and add them together and set the sum equal to 60, like this: x + 2x = 60. Combining like terms, we get 3x = 60, and dividing both sides by 3, we get x = 20. So the smaller number is 20, and 2x, which is the larger number, is 2 ·20, which is 40. Checking both of these numbers by adding them together, they give us a sum of 60 so we know we have the correct numbers.

Answer 2

This is a systems of equations problem.

Let x and y represent the two numbers.

The sum of two numbers is 60:

x + y = 60

The larger number is twice the smaller number. Let x be the larger number:

x = 2y

Find the numbers

Substitute 2y for x in the first equation:

2y + y = 60

3y = 60

y = 20

Plug in 20 for y:

x + 20 = 60

Subtract:

x = 60 - 20 = 40

So y = 20 and x = 40.