There were some children in a concert hall.
13 of the children lined up in 8 short rows and
15 of the children lined up in 4 long rows. The remaining children did not line up. There are 12 more children in each long row than each short row.
(a) What fraction of the children did not line up?
(b) How many children lined up?
|
Short rows |
Long 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 -
13 -
15 = 1 -
515 -
315= 1 -
815=
715(b)
515 of the children lined up in short rows.
8 u = 5 p --- (1)
315 of the children lined up in long rows.
4 u + 48 = 3 p --- (2)
(1)
x3
24 u = 15 p --- (3)
(2)
x5
20 u + 240 = 15 p --- (4)
(3) = (4)
24 u = 20 u + 240
24 u - 20 u = 240
4 u = 240
1 u = 240 ÷ 4 = 60
Number of children who lined up
= 8 u + 4 u + 48
= 12 u + 48
= 720 + 48
= 768
Answer(s): (a)
715; (b) 768