A bag contained black, grey and white pens.
25 of the pens were black and
49 of the remainder were grey pens.The rest were white pens.
- Find the ratio of the number of white pens to the number of black pens.
- There were 174 fewer grey pens than black pens. How many pens were there in the bag?
| Black pens |
Grey pens |
White pens |
| 2x3 |
3x3 |
| |
4x1 |
5x1 |
| 6 u |
4 u |
5 u |
(a)
Fraction of black pens =
25 Fraction of pens that are not black = 1 -
25 =
35Remaining fraction of grey pens =
49Remaining fraction of white pens = 1 -
49 =
59The total number of grey pens and white pens is the repeated identity.
Make the repeated identity the same by using LCM.
LCM of 3 and 9 = 9
White pens : Black pens
5 : 6
(b)
Difference in the number of black pens and grey pens
= 6 u - 4 u
= 2 u
2 u = 174
1 u = 174 ÷ 2 = 87
Total number of pens
= 6 u + 4 u + 5 u
= 15 u
= 15 x 87
= 1305
Answer(s): (a) 5 : 6; (b) 1305
