Question

What is the number expressed by forty-eight decreased by a number is the same as the difference of four times the number and seven?

Answer 1

`11`

Explanation:

To turn this into an equation, here are some tips:

1. "Decreased by" means subtraction
2. "Is" means equals
3. "Difference" means a subtraction of two things
4. Give things you don't know a variable. Since they are talking about a "number", I will use the variable `n`

`stackrel(48)overbrace"48"color(white)"x" stackrel(-)overbrace"decreased" color(white)"x"stackrel(n)overbrace"by a number"color(white)"x" stackrel(=)overbrace"is the same as"color(white)"x" stackrel(4n - 7)overbrace"the difference of four time the number and seven"`

`48 - n = 4n - 7`

Now solve the problem by isolating `n` to one side:

`48 - n = 4n - 7`

`48 = 5n - 7`

`55 = 5n`

`11 = n`

The number is `11`.