# Thread: A is two-third of the sum of B and C. B is three-quarter of the sum of A and C.

1. ## A is two-third of the sum of B and C. B is three-quarter of the sum of A and C.

A is two-third of the sum of B and C. B is three-quarter of the sum of A and C. Express A as a fraction of B.

2. ## Simultaneous equations

Hello dtay

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Originally Posted by dtay
A is two-third of the sum of B and C. B is three-quarter of the sum of A and C. Express A as a fraction of B.
You need to create two equations involving $\displaystyle A, B$ and $\displaystyle C$, and then eliminate $\displaystyle C$ to find an equation involving just $\displaystyle A$ and $\displaystyle B$.

Here are some clues:

The first statement can be written: $\displaystyle A = \tfrac23(B+C)$

So if we multiply by $\displaystyle 3: 3A = 2B+2C$

$\displaystyle \Rightarrow C = \tfrac32A - B$ (1)

Now write down the second statement in a similar way, and use equation (1) to eliminate $\displaystyle C$.

Then re-arrange so that you have $\displaystyle A$ on one side, and $\displaystyle B$ on the other. Finally, divide both sides by $\displaystyle B$ to find $\displaystyle \frac{A}{B}$. I get the answer:

$\displaystyle \frac{A}{B}= \frac{14}{15}$

Can you fill in the gaps?