At a carnival, the children were put into two groups. 45 of Group F were boys and 34 of Group G were girls. Group G had twice as many children as Group F. There were 12 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 |
1x5x2 = 10 u |
2x5x2 = 20 u |
3x5x2 = 30 u |
Boys |
Girls |
Boys |
Girls |
|
4x2 |
1x2 |
1x5 |
3x5 |
|
8 u |
2 u |
5 u |
15 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 5 is 5.
The number of children in Group G is repeated. Make the number of children in Group G the same. LCM of 4 and 10 is 20.
BoysTotal =
8 + 510 + 20 =
1330 (b)
Number of fewer boys in Group F than Group G
= 8 u - 5 u
= 3 u
3 u = 12
1 u = 12 ÷ 3 = 4
Total number of children
= 30 x 4
= 120
Answer(s): (a)
1330; (b) 120