Betty had 70 pens.
37 were yellow and the rest were pink and gold. The ratio of the number of pink pens to the number of gold pens was 1 : 4. Betty decided to buy some more yellow pens to increase the number of yellow pens to half of the total number of pens.
- How many less pink pens than yellow pens did he have at first?
- How many more yellow pens did he have to buy?
| Yellow pens |
Pink pens |
Gold pens |
Total |
| 3x5 |
4x5 |
|
| |
1x4 |
4x4 |
|
| 15 u |
4 u |
16 u |
70 |
| |
Yellow pens |
Pink pens |
Gold pens |
| Before |
15 u |
4 u |
16 u |
| Change |
+ ? |
|
|
| After |
20 u |
20 u |
Comparing yellow, pink
and gold pens
in the end |
1 |
1 |
(a)
The total number of pink pens and gold pens is repeated. Make the total number of pink pens and gold pens the same. LCM of 4 and 5 is 20.
Total number of pens at first
= 15 u + 4 u + 16 u
= 35 u
35 u = 70
1 u = 70 ÷ 35 = 2
Number of less pink pens than yellow pens at first
= 15 u - 4 u
= 11 u
= 11 x 2
= 22
(b)
Number of more yellow pens that Betty had to buy
= 20 u - 15 u
= 5 u
= 5 x 2
= 10
Answer(s): (a) 22; (b) 10
