Question

The difference between two-fifth of a number and 9 is 7. Find the number.

Answer 1

The number is 40.

Explanation:

Step 1: Assume your variables

Consider the 'number' to be
`x`.

Step 2: Create an equation(s)

The information in the question states that the difference between
`(2)/(5)` of
`x` and
`9`, is
`7`.

Representing this mathematically gives us:

`((2)/(5)* x) -9=7`

Step 3: Solve the equation

The equation we have is:

`((2)/(5)* x) -9=7`

So, let's solve it:

`((2)/(5)* x) -9=7\\\\\text{Add 9 to both sides:}\\((2)/(5)* x) -9+9=7+9\\\\\text{Simplify:}\\((2)/(5)* x)=16\\\\\text{Multiply by}~(5)/(2)~\text{on both sides:}\\(5)/(2)*(2)/(5)* x=16* (5)/(2)\\\\\text{Simplify:}\\1* x=(80)/(2)\\\\\text{Calculate:}\\x=40`