Zara, Gabby and Hilda have equal number of pencils. Zara packs all her pencils equally into 9 packets. Gabby packs all her pencils equally into 6 packets. Hilda packs all her pencils equally into 3 packets. 6 packets of Zara's pencils, 5 packets of Gabby's pencils and 2 packets of Hilda's pencils add up to 390 pencils. How many pencils do they have altogether?
| |
Zara |
Gabby |
Hilda |
| Number of packets |
9 |
6 |
3 |
| Number of pencils |
18 u |
18 u |
18 u |
| Number of pencils in each packet |
2 u |
3 u |
6 u |
All the pencils can be put into the packets without remainder.
All the children have equal numbers of pencils.
Make the number of pencils that each child has the same. LCM of 9, 6 and 3 = 18
Number of pencils that each child has = 18 u
Number of pencils in 1 packet of Zara's pencils = 18 u ÷ 9 = 2 u
Number of pencils in 1 packet of Gabby's pencils = 18 u ÷ 6 = 3 u
Number of pencils in 1 packet of Hilda's pencils = 18 u ÷ 3 = 6 u
Number of pencils in 6 packets of Zara's pencils, 5 packets of Gabby's pencils and 2 packets of Hilda's pencils
= (6 x 2 u) + (5 x 3 u) + (2 x 6 u)
= 12 u + 15 u + 12 u
= 39 u
39 u = 390
1 u = 390 ÷ 39 = 10
Total number of pencils that they have
= 3 x 18 u
= 54 u
= 54 x 10
= 540
Answer(s): 540
