Question:

When one-fourth of a number is added to one-third of the same number, the result is 28. What is the number?

I am a student, in grade 10.



Hi,

The problem with quarters and thirds is that you can't add them directly. On the measuring cup I use for baking there is a scale that tells me one-fourth of a cup and another that tells me one-third of a cup but no scale that allows me to measure one-third of a cup plus one-fourth of a cup. I know that 3 x 4 = 12 so if there were a scale that measured twelfths of a cup I could do it. One-fourth is three-twelfths and one-third is four-twelfths so

 1/4 + 1/3 = 3/12 + 4/12 = 7/12

You don't have cups but the idea is the same. There some unknown number you need to find. In order to talk about this number give it a name. Call it x. What you then know is that

one-quarter of x plus one-third of x is 28 that is  1/4 x + 1/3 x = 28 But  1/4 + 1/3 = 7/12 so  7/12 x = 28

Now since 4 x 7 = 28,

 1/12 x = 4 and thus x is 48.

Now you should check, does one-fourth of a 48 added to one-third of 48 give 28?

Cheers,
Penny

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