The total volume of water in Bottle Q, Bottle R and Bottle S was 74 mℓ. Ian poured out half the volume of water from Bottle Q, doubled the amount of water in Bottle R and added 78 mℓ of water into Bottle S. The ratio of the volume of water in Bottle Q to Bottle R to Bottle S is now 1 : 4 : 4. Find the total volume of water in the three bottles now.
| |
Q |
R |
S |
| Before |
2 u |
2 u |
4 u - 78 |
| Change |
- 1 u |
+ 2 u |
+ 78 |
| After |
1 u |
4 u |
4 u |
Volume of water in Bottle Q at first before Archie poured out half the volume
= 2 x 1 u
= 2 u
Volume of water in Bottle R at first before Archie doubled the volume
= 4 u ÷ 2
= 2 u
Volume of water in Bottle R at first before Archie added 78 mℓ of water
= 4 u - 78
Total volume of water in the three bottles at first
= 2 u + 2 u + 4 u - 78
= 8 u - 78
8 u - 78 = 74
8 u = 74 + 78
8 u = 152
1 u = 152 ÷ 8 = 19
Total volume of water in the three bottles now
= 1 u + 4 u + 4 u
= 9 u
= 9 x 19
= 171 mℓ
Answer(s): 171 mℓ
