Question

Set up the equation for the following word problem and solve the equation. Let z be the unknown number.51 times the difference between a number and 21 is equal to the number plus 58.

Answer 1

You have the following sentence:

51 times the difference between a number and 21 is equal to the number plus 58.​

The previous expression can be written in an algebraic way as follow:

If z is the unknown number, you have:

`51\cdot(z-21)=z+58`

In order to solve the previous expression, proceed as follow:

- Expand parenthesis left side:

`51z-1071=z+58`

- Next, subtract z both sides and add 1071 both sides:

`51z-z=58+1071`

- Simplify like terms;

`50z=1129`

- Divide by 50 both sides:

`z=(1129)/(50)\approx22.58`

Hence, the value of z is 1129/50, or approximately 22.58