The total number of beads in Box F, Box G and Box H was 147.
27 of the beads from Box F and 27 beads from Box G were removed. More beads were then added into Box H until the number of beads in it was quadrupled. The ratio of the number of beads in Box F to Box G to Box H became 5 : 4 : 4.
- How many more beads were there in Box F than Box G at first?
- Find the total number of beads in Box F and Box H in the end.
|
Box F |
Box G |
Box H |
Total |
Before |
7 u |
4 u + 27 |
1 u |
147 |
Change |
- 2 u |
- 27 |
+ 3 u |
|
After |
5 u |
|
4 u |
|
Comparing the beads in the end |
5 u |
4 u |
4 u |
|
(a)
Total number of beads at first
= 7 u + 4 u + 27 + 1 u
= 12 u + 27
12 u + 27 = 147
12 u = 147 - 27
12 u = 120
1 u = 120 ÷ 12 = 10
Number of more beads in Box F than Box G at first
= 7 u - (4 u + 27)
= 7 u - 4 u - 27
= 3 u - 27
= 3 x 10 - 27
= 30 - 27
= 3
(b)
Total number of beads in Box F and Box H in the end
= 5 u + 4 u
= 9 u
= 9 x 10
= 90
Answer(s): (a) 3; (b) 90