Laura is 2 inches taller than Rebecca. Max is 4 inches taller than Rebecca. The total height for the three girls is 150 inches. How tall is Rebecca?
I am having trouble figuring out Rebecca's height because I do not know how to use the given information effectively.
Can anyone give me a hint on how to make a good start? I'm stuck.
On
The total height is three Rebeccas and some extras, $2$in and $4$in, that is, extra $6$in. And that is $150$in. So three Rebeccas make $150-6=144$in. Divide $144$in by $3$ and get $$\text{Rebecca} \ \ \frac{144}{3}= 48\text{in}\\ \text{Laura}\ \ 48\text{in} + 2\text{in} = 50\text{in}\\ \text{Max} \ \ 48\text{in} + 4\text{in} = 52\text{in}$$
Now that we see the results, it's clearer. In fact, Laura's height is less by $2$ than Max's and larger by $2$ than Rebecca's, so that is exactly in the middle. Therefore, Laura's height has to be the average of the three, $\frac{150}{3}=50$in, and so, again, Rebecca's height is $48$in.
$$r+l+m=150$$ because the heights add up to 150. $$r+2=l$$ because Rebecca is 2 inches shorter than Laura $$r+4=m$$ because Rebecca is 4 inches shorter than Max Substitution into the first equation gives $$r+(r+2)+(r+4)=150$$
Where $r,l,m$ is the respective heights of the girls.
Can you take it from there?