Question

The sum of two numbers is 51. One number is 15 more than the other. What is the smaller number. Try solving this by writing a system of equations and substitution.

Answer 1

Let's convert the given relationships into an equation.

Let's name the two number x and y.

The sum of the two numbers is 51: x + y = 51

One number is 15 more than the other: x = y + 15

Using the equations that we generated from the given relationships, let's determine the value of the two numbers by substitution.

Let's substitute x = y + 15 to x + y = 51.

`\text{ x + y = 51 }\rightarrow\text{ (y + 15) + y = 51}`
`\text{ y + 15 + y = 51 }\rightarrow\text{ 2y = 51 - 15}`
`\text{ 2y = 36 }\rightarrow\text{ y = }(36)/(2)`
`\text{ y = 18}`

Since we now get the value of y, y = 18, let's determine the value of x.

`\text{ x = y + 15 }\rightarrow\text{ x = 18 + 15}`
`\text{ x = 33}`

Therefore, the value of the two numbers is 18 and 33.