There are six times as many children as adults in a concert hall. There are 172 more boys than girls. If there are 441 people in the concert hall,
- how many children are there?
- how many girls are there?
- how many boys are there?
| Children |
Adults |
Total |
| 6 u |
1 u |
7 u |
| Girls |
Boys |
|
|
| 1 p |
1 p + 172 |
|
|
(a)
Number of adults = 1 u
Number of children = 6 x 1 u = 6 u
Total number of people
= 6 u + 1 u
= 7 u
7 u = 441
1 u = 441 ÷ 7 = 63
(a)
Number of children
= 6 u
= 6 x 63
= 378
(b)
Number of girls = 1 p
Number of boys = 1 p + 172
1 p + 1 p + 172 = 378
2 p + 172 = 378
2 p = 378 - 172
2 p = 206
1 p = 206 ÷ 2 = 103
Number of girls
= 1 p
= 103
(c)
Number of boys
= 1 p + 172
= 103 + 172
= 275
Answer(s): (a) 378; (b) 103; (c) 275
