The total number of beads in Box R, Box S and Box T was 108.
25 of the beads from Box R and 12 beads from Box S were removed. More beads were then added into Box T until the number of beads in it was quadrupled. The ratio of the number of beads in Box R to Box S to Box T became 3 : 2 : 4.
- How many more beads were there in Box R than Box S at first?
- Find the total number of beads in Box R and Box T in the end.
|
Box R |
Box S |
Box T |
Total |
Before |
5 u |
2 u + 12 |
1 u |
108 |
Change |
- 2 u |
- 12 |
+ 3 u |
|
After |
3 u |
|
4 u |
|
Comparing the beads in the end |
3 u |
2 u |
4 u |
|
(a)
Total number of beads at first
= 5 u + 2 u + 12 + 1 u
= 8 u + 12
8 u + 12 = 108
8 u = 108 - 12
8 u = 96
1 u = 96 ÷ 8 = 12
Number of more beads in Box R than Box S at first
= 5 u - (2 u + 12)
= 5 u - 2 u - 12
= 3 u - 12
= 3 x 12 - 12
= 36 - 12
= 24
(b)
Total number of beads in Box R and Box T in the end
= 3 u + 4 u
= 7 u
= 7 x 12
= 84
Answer(s): (a) 24; (b) 84