# Thread: How to find the greater part of the following equation

1. ## How to find the greater part of the following equation

184 is divided into two parts such that one-third of one part may exceed one-seventh of the other part by 8, then the greater part is _______.

The possible answers are 72, 110, 112, 114.

I have tried this question in several ways, but I am unable to solve this question. Can someone point me in the right direction.

2. ## Re: How to find the greater part of the following equation

You have to solve following system of equations :

$x+y=184$

$\frac{1}{3}\cdot x= \frac{1}{7} \cdot y + 8$

3. ## Re: How to find the greater part of the following equation

thanks that helps.

4. ## Re: How to find the greater part of the following equation

I'll continue where princeps ended his reply.

x + y = 184..........Equation A
(x/3) = (y/7) + 8...Equation B

I will solve Equation A for either x or y. How about for y?

x + y = 184

y = 184 - x

I will now plug that for y in Equation B to find the value of x.

(x/3) = [(184 - x)/7)] + 8

Multiply by 21 to clear the fractions on both sides of the equation.

After doing so, we get

7x = 3(184 - x) + 8(21)

7x = 552 - 3x + 168

7x = -3x + 720

7x + 3x = 720

10x = 720

x = 720/10

x = 72

Let x = 72 in either Equation A or B above.

I will use Equation A.

x + y = 184

72 + y = 184

y = 184 - 72

y = 112

Which is the answer? Can you tell me given the amount of work that was done?

,

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### divide 184 into two parts such that one-thirds of one part may exceed one-seventh of the other part by 8.

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