At a carnival, the children were put into two groups. 45 of Group X were girls and 23 of Group Y were boys. Group Y had twice as many children as Group X. There were 18 fewer girls in Group X than Group Y.
- What fraction of the total number of children at the carnival were girls? Give your answer in the simplest form.
- What was the total number of children at the carnival?
Group X |
Group Y |
Total |
1x5x3 = 15 u |
2x5x3 = 30 u |
3x5x3 = 45 u |
Girls |
Boys |
Girls |
Boys |
|
4x3 |
1x3 |
1x10 |
2x10 |
|
12 u |
3 u |
10 u |
20 u |
|
(a)
The number of children in Group X is repeated. Make the number of children in Group X the same. LCM of 1 and 5 is 5.
The number of children in Group Y is repeated. Make the number of children in Group Y the same. LCM of 3 and 10 is 30.
GirlsTotal =
12 + 1015 + 30 =
2245 (b)
Number of fewer girls in Group X than Group Y
= 12 u - 10 u
= 2 u
2 u = 18
1 u = 18 ÷ 2 = 9
Total number of children
= 45 x 9
= 405
Answer(s): (a)
2245; (b) 405