There were some children in a concert hall.
14 of the children lined up in 8 long rows and
15 of the children lined up in 4 short rows. The remaining children did not line up. There are 12 more children in each short row than each long row.
(a) What fraction of the children did not line up?
(b) How many children lined up?
|
Long rows |
Short rows |
Number |
8 |
4 |
Value |
1 u |
1 u + 12 |
Total value |
8 u |
4 u + 48 |
(a)
Fraction of children who did not line up
= 1 -
14 -
15 = 1 -
520 -
420= 1 -
920=
1120(b)
520 of the children lined up in long rows.
8 u = 5 p --- (1)
420 of the children lined up in short rows.
4 u + 48 = 4 p --- (2)
(1)
x4
32 u = 20 p --- (3)
(2)
x5
20 u + 240 = 20 p --- (4)
(3) = (4)
32 u = 20 u + 240
32 u - 20 u = 240
12 u = 240
1 u = 240 ÷ 12 = 20
Number of children who lined up
= 8 u + 4 u + 48
= 12 u + 48
= 240 + 48
= 288
Answer(s): (a)
1120; (b) 288