Question

The ratio of soccer players to volleyball players n the bus was 5:3. If there were a total of 48 players on the bus, how many were volleyball players?

Answer 1

Answer: 18

Work Shown

x = number of volleyball players

48-x = number of soccer players

(48-x)/x = 5/3

3(48-x) = 5x

144-3x = 5x

144 = 5x+3x

144 = 8x

8x = 144

x = 144/8

x = 18 which is the final answer.

Here is another approach we could do.

The ratio 5:3 can be scaled up to 5k:3k for some positive integer k.

This would mean there are 5k soccer players and 3k volleyball players.

Those values must add to 48 players total.

5k+3k = 48

8k = 48

k = 48/8

k = 6

So there are...

• 5k = 5*6 = 30 soccer players
• 3k = 3*6 = 18 volleyball players

As a check, 30+18 = 48, so the answer is confirmed.

Also note that the ratio 30:18 reduces to 5:3 when dividing both parts by the GCF 6.

Answer 2

18 volleyball players

Explanation:

If the ratio of soccer players to volleyball players on the bus was 5:3, then there were 5+3 = 8 parts in the ratio.

Since the total number of players on the bus was 48, then there were 48/8 = 6 players in each part of the ratio.

Therefore, there were 6 × 3 = 18 volleyball players on the bus.