Question

c) one fourth of a number x is added to one third of the same number ​

Answer 1

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

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➡️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.

$\huge \colorbox{green}{cheers}$

Answer 2

Given : One fourth of a number x is added to one third of the same number.​

To Find : Expression and simplify

Solution:

One fourth of a number x  = x/4

one third of the same number.​ = x/3

One fourth of a number x is added to one third of the same number.​

= x/4  + x/3

Expression is  x/4  + x/3  

Simplifying  Expression

x/4  + x/3  

LCM of denominator = 12

= ( 3x + 4x)/12

= 7x/12

Expression is  x/4  + x/3  

Simplified 7x/12

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