What are two numbers that add up to 36 and when they're in proportional format equal 3/4?For example, 2 numbers that add up to 24 and when they're in proportional format equal 2, are 16 and 8.

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kellimartin's profile pic

kellimartin | High School Teacher | (Level 1) Adjunct Educator

Posted on

When numbers are in proportion to each and in reduced form, then at some point they had to have a number in common that would then reduce to 3/4.

Consider this number x.  So, before it was reduced, we know that the proportion looked like this:  3x/4x and we also know that the sum is 36.  Therefore, 3x + 4x =36

Thus, 7x = 36 and x = 36/7

Putting this back into the proportion of 3/4, you have 3(36/7) and 4(36/7), which means the two numbers are:

108/7 and 144/7.

This process is used quite a bit in Geometry in the study of proportional figures and angles.

krishna-agrawala's profile pic

krishna-agrawala | College Teacher | (Level 3) Valedictorian

Posted on

The two numbers will not be whole numbers.

Questions of this type can be solved using the following general steps.

If two numbers add x and y are such that:

x + y = N and

x/y = a/b

Then:

x = N*[a/(a + b)]

y = N*[b/(a + b)]

In the above question:

a = 3, b = 4, and N = 36

Therefor:

x = 36*3/(3 + 4) =  36*3/7 = 108/7

y = 36*4/(3 + 4) =  36*4/7 = 114/7

x + y = N = 108/7 + 144/7 = (108 +144)/7 = 252/7 = 36

neela's profile pic

neela | High School Teacher | (Level 3) Valedictorian

Posted on

We assume that one number is x and the other is 3x/4 so that their ratio is 3/4.

Their algebraic sum = x+(3x/4) =7x/4 which is equal to 36 by hypothesis.

Therefore, 7x/4 = 36 or

7x=36*4 or

x=36*4/7 = 144/7 and  the other numver,3x/4 = (3/4)*144/7 =108/7

The numbers are 144/7  and 108/7.

Aliter: 1 is distrinbeted in the format m/n or p:q implies,

p/(p+q)) and q/(p+q). So if N is to be distributed in this prportion, then Np/((p+q) and Nq/(p+q) are the required results. Putting p=1 and q= 3/4 you get:36*1/(1+3/4)  = 36*4/7 and 36*(3/4)/(1+3/4) = 36*3/7 are the required results.

 

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