At a carnival, the children were put into two groups. 45 of Group D were boys and 23 of Group E were girls. Group E had twice as many children as Group D. There were 16 fewer boys in Group D than Group E.
- 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 D |
Group E |
Total |
1x5x3 = 15 u |
2x5x3 = 30 u |
3x5x3 = 45 u |
Boys |
Girls |
Boys |
Girls |
|
4x3 |
1x3 |
1x10 |
2x10 |
|
12 u |
3 u |
10 u |
20 u |
|
(a)
The number of children in Group D is repeated. Make the number of children in Group D the same. LCM of 1 and 5 is 5.
The number of children in Group E is repeated. Make the number of children in Group E the same. LCM of 3 and 10 is 30.
BoysTotal =
12 + 1015 + 30 =
2245 (b)
Number of fewer boys in Group D than Group E
= 12 u - 10 u
= 2 u
2 u = 16
1 u = 16 ÷ 2 = 8
Total number of children
= 45 x 8
= 360
Answer(s): (a)
2245; (b) 360