A student finished 8 of her homework problems in class. If the ratio of problems she finished to...

Question:

A student finished {eq}8 {/eq} of her homework problems in class.

If the ratio of problems she finished to problems she still had left was {eq}4: 1 {/eq}, how many homework problems did she have total?

Estimating the Total Number of Homework Problems:

The ration is commonly used for comparing two or more values. Here, let's consider the homework problem, which she has to do is, {eq}x. {/eq} Now from the given information, we need to form an equation to solve the value of {eq}x. {/eq} Hence we need to calculate the total number of homework problems, though we need to add the {eq}x {/eq} value with the homework problems, which were already completed by her to get the total value.

Completed homework problems {eq}=8. {/eq}

Homework problems yet to be completed is {eq}=x. {/eq}

And the ratio of the completed problems: problems yet to completed is,

{eq}8:x {/eq}

Now equate this with the given ratio,

{eq}8:x=4:1 \\ x=\frac{8}{4} \\ x=2 {/eq}

Therefore the total number of homework problems is, {eq}8+x \\ 8+2=10. {/eq}