Ratio P6 Rosyth 2011 SA2 P2 Q11

Fraction P6 2010 SA1 Rosyth P2 Q18

There were 156 more pupils in the playground than in the library. 1/5 of the pupils in the library were girls and 5/6 of the pupils in the playground were boys. If there were 17 more girls in the playground than in the library, find the total number of pupils in the two places.


You may start with
a) There were 156 more pupils in the playground than in the library, or
b) there were 17 more girls in the playground than in the library



1/5 of the pupils in the library were girls --> 5 units in library with 1 unit girls
5/6 of the pupils in the playground were boys --> 6 UNITS in playground, with 1 UNIT girls
Note: unit and UNIT are not the same

a)
There were 156 more pupils in the playground than in the library
Draw 6 UNITS for playground + 156 [divided in 6 parts]
Draw 6 UNITS for library, but with 1 UNIT divided into 5 parts

P [   ][   ][   ][   ][   ][   ][][][][][][]
L [   ][   ][   ][   ][   ][||||]<---156--->

156  ÷  6  = 26

Compare the girls in the playground and library
      26 [   ][ ]
[   ][|
       17

26  - 17  =  9

1 u -->  9  x  5  =  45  Compare the 6 UNITS of playground with 6 UNITS of libary

6 u -->  6  x  45  =  170


270  +  156  +  270  =  696  pupils


There were 696 pupils.



Alternative solution (b)
----------------------------
there were 17 more girls in the playground than in the library


[ ][17]
[ ]


[][17] [][17] [][17] [][17] [] [17] [][17]
[] [] [] [] [] <------------156------------>




6 u  +  17 x 6  -->  5 u  +  156


1 u  -->  156  -  102  =  54


5 u  -->  5  x  54  =  270


270  +  270  +  156  =  696 pupils


There were 696 pupils.

Rates P6 2010 SA2 Rosyth P2 Q16

Machine A and B each printed a fixed number of newspaper per hour. Machine B started printing earlier at a rate of 75 copies per hour. After Machine B had printed for 10 hours, Machine A had printed 340 copies. After Machine B had printed for 16 hours, Machine A had printed 886 copies. (a) How many copies of newspaper did Machine A print per hour? (b) How long would Machine B have worked when both machines have printed a total of 2750 copies? [5 marks][Answer given: 91 copies, 20 hours]


B1: 10 h --> 10 x 75 = 750 copies
A1: ? h --> 340 copies

B2: 16 h --> 16 x 75 = 1200 copies
A2: ? + 6 h --> 886 copies

A: 6 h --> 886 - 340 = 546 copies
     1 h --> 546/6 = 91 copies

a) It was 91 copies.


A + B : 1 h --> 91 + 75 = 166 copies

2750 - 750 - 340 = 1660 copies

1660/166 = 10 h

10 + 10 = 20 h

b) It was 20 h.