Question

A student finished 45 of her homework problems in class. If the ratio of problems shefinished to problems she still had left was 9:4, how many homework problems did shehave total?

Answer 1

The ratio between the amount of problems she finished and the problems she still had left is given by the division between those amount. Since this ratio is 9:4, if we call the amount of homework she still has left as x, we have the following relation

`(45)/(x)=(9)/(4)`

Solving for x, we have

`\begin{gathered} (45)/(x)=(9)/(4) \\ (x)/(45)=(4)/(9) \\ x=(4)/(9)\cdot45 \\ x=(4\cdot45)/(9) \\ x=(180)/(9) \\ x=20 \end{gathered}`

She still has 20 problems left to solve. The total amount of problems is given by the sum between the problems she already finished and the problems left to solve, then, the total amount of problems is

`45+20=65`

65 problems.