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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.

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  • $\begingroup$ $x+x+2+x+4=150$ $\endgroup$
    – Math137
    Jan 29, 2015 at 0:26

2 Answers 2

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$$r+l+m=150$$ 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?

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    $\begingroup$ It may help to elaborate on how you got $r+(r+2)+(r+4)$--given the level of the OP's question, if he or she can't get how to quickly do this, then I imagine he or she will have an equally difficult time understanding your derivation. :) $\endgroup$
    – Daniel W. Farlow
    Jan 29, 2015 at 3:45
  • $\begingroup$ Nice. More understandable for the OP I would imagine. I was thinking about writing up an answer where we kind of forgot about "details" for a moment and had (1) Laura = Rebecca + 2, (2) Rebecca = Rebecca, and (3) Max = Rebecca + 4. Then we would have (Rebecca + 2) + Rebecca + (Rebecca + 4) = 150, and you can see that 3 Rebecca + 6 = 150 which would imply that Rebecca = 144/3 = 48. A very dirty answer, of course, but I think that would be quite clear to the OP. Pedagogy...so interesting! Nice answer though :) $\endgroup$
    – Daniel W. Farlow
    Jan 29, 2015 at 5:06
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    $\begingroup$ That seems like such a laborious way of going about it though. I'm surprised I haven't seen anything on this. Granted, comments are not the ideal place for extended mathematical treatments. Is that intentional you think? I might have to do some more investigating and then perhaps frame a good question for Meta. Because right now it's difficult to have beautifully typeset comments (at least in an easy fashion). :/ $\endgroup$
    – Daniel W. Farlow
    Jan 29, 2015 at 5:43
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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.

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