Question

Bag A contains 5x coins.
Bag B contains 3x coins.
8 coins are taken from Bag B and put into Bag A
The ratio of coins in Bag A to Bag B is now 11:5
Work out the total number of coins.

Answer 1

Answer:

given ,

number of coins in bag A = 5x

number of coins in bag B = 3x

_____________________________________

According to Question ,

8 coins are taken from Bag B and put into Bag A

The ratio of coins in Bag A to Bag B is now 11 : 5

therefore ,

$\frac{5x + 8}{3x - 8} = \frac{11}{5} \\ \\ 5(5x + 8) = 11(3x - 8) \\ \\ 25x + 40 = 33x - 88 \\ \\ 33x - 25x = 40 + 88 \\ \\ 8x = 128 \\ \\ x = \cancel\frac{128}{8} \\ \\ \fbox{x =16}$

now ,

$no. \: of \: coins \: in \: bag \: A = 5x \\ \dashrightarrow{5 \times 16 = 80 \: coins}$

$number \: of \: coins \: in \: bag \: B = 3x \\ \dashrightarrow{3 \times 16 = 48 \: coins}$

$total \: number \: of \:coins = 80 + 48 \\ \dashrightarrow{ 128 \: coins}$

hope helpful :D