# 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

Welcome to Math Help Forum!
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 $A, B$ and $C$, and then eliminate $C$ to find an equation involving just $A$ and $B$.

Here are some clues:

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

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

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

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

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

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

Can you fill in the gaps?