Question

Natalie gets pocket money from her mother and is

planning to buy a dress for her annual day celebrations
in school. Had she got $10 more pocket money from her
mom, the amount would have been 9 times the square of
the money she has now. How much money does she have
now?

Answer 1

Natalie has $1.11 right now.

Explanation:

1. Create an equation that represents Natalie's situation. Let x = the money Natalie has right now.

`x+ 10 = 9(x)^2`

2. This equation is a quadratic, so we need to factorise to solve for x, the amount of money Natalie has right now.

3.
`x + 10 = 9x^2`

4.
`0 = 9x^2 -x - 10`

5.
`0 = 9x^2 + 9x -10x - 10`

6.
`0 = 9x(x+1) -10(x+1)`

7.
`0 = (9x-10) (x+1)`

8.
`x+ 1 = 0\\\\x = -1`

9.
`9x - 10 = 0\\9x = 10\\x = 10/9, 1.11`

10. The amount of money Natalie has now cannot be negative. Therefore, Natalie has $1.11 right now.