At a carnival, the children were put into two groups. 34 of Group F were boys and 45 of Group G were girls. Group G had thrice as many children as Group F. There were 30 fewer boys in Group F than Group G.
- What fraction of the total number of children at the carnival were boys? Give your answer in the simplest form.
- What was the total number of children at the carnival?
Group F |
Group G |
Total |
1x4x5 = 20 u |
3x4x5 = 60 u |
4x4x5 = 80 u |
Boys |
Girls |
Boys |
Girls |
|
3x5 |
1x5 |
1x12 |
4x12 |
|
15 u |
5 u |
12 u |
48 u |
|
(a)
The number of children in Group F is repeated. Make the number of children in Group F the same. LCM of 1 and 4 is 4.
The number of children in Group G is repeated. Make the number of children in Group G the same. LCM of 5 and 12 is 60.
BoysTotal =
15 + 1220 + 60 =
2780 (b)
Number of fewer boys in Group F than Group G
= 15 u - 12 u
= 3 u
3 u = 30
1 u = 30 ÷ 3 = 10
Total number of children
= 80 u
= 80 x 10
= 800
Answer(s): (a)
2780; (b) 800