A bag contained black, purple and yellow pens.
25 of the pens were black and
38 of the remainder were purple pens.The rest were yellow pens.
- Find the ratio of the number of yellow pens to the number of black pens.
- There were 154 fewer purple pens than black pens. How many pens were there in the bag?
| Black pens |
Purple pens |
Yellow pens |
| 2x8 |
3x8 |
| |
3x3 |
5x3 |
| 16 u |
9 u |
15 u |
(a)
Fraction of black pens =
25 Fraction of pens that are not black = 1 -
25 =
35Remaining fraction of purple pens =
38Remaining fraction of yellow pens = 1 -
38 =
58The total number of purple pens and yellow pens is the repeated identity.
Make the repeated identity the same by using LCM.
LCM of 3 and 8 = 24
Yellow pens : Black pens
15 : 16
(b)
Difference in the number of black pens and purple pens
= 16 u - 9 u
= 7 u
7 u = 154
1 u = 154 ÷ 7 = 22
Total number of pens
= 16 u + 9 u + 15 u
= 40 u
= 40 x 22
= 880
Answer(s): (a) 15 : 16; (b) 880
