The sum of two numbers is 55. Two times the smaller number plus forty-six is the larger number. What are the numbers?

Question

The sum of two numbers is 55. Two times the smaller number plus forty-six is the larger number. What are the numbers?

Answer 1

Let's let x represent the smaller number and y represent the larger number. Then we can write the following equations using the information in the problem:

x + y = 55

2x + 46 = y

Now we can use substitution to solve this system of equations.

Substitute the expression 2x + 46 for y in the first equation:

x + y = 55

x + 2x + 46 =55

Now combine like terms and use inverse operations to find the value of x:

x + 2x + 46 = 55

3x + 46 = 55

3x + 46 - 46 = 55 - 46

3x = 9

3x/3 = 9/3

x = 3

So the smaller number is 3

The larger number will be 52 (or 55-3)

Note that 2 * 3 + 46 = 6 + 46 =52