Rachel, Fanny and Natalie have equal number of pencils. Rachel packs all her pencils equally into 4 packets. Fanny packs all her pencils equally into 9 packets. Natalie packs all her pencils equally into 6 packets. 3 packets of Rachel's pencils, 6 packets of Fanny's pencils and 2 packets of Natalie's pencils add up to 504 pencils. How many pencils do they have altogether?
| |
Rachel |
Fanny |
Natalie |
| Number of packets |
4 |
9 |
6 |
| Number of pencils |
36 u |
36 u |
36 u |
| Number of pencils in each packet |
9 u |
4 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 4, 9 and 6 = 36
Number of pencils that each child has = 36 u
Number of pencils in 1 packet of Rachel's pencils = 36 u ÷ 4 = 9 u
Number of pencils in 1 packet of Fanny's pencils = 36 u ÷ 9 = 4 u
Number of pencils in 1 packet of Natalie's pencils = 36 u ÷ 6 = 6 u
Number of pencils in 3 packets of Rachel's pencils, 6 packets of Fanny's pencils and 2 packets of Natalie's pencils
= (3 x 9 u) + (6 x 4 u) + (2 x 6 u)
= 27 u + 24 u + 12 u
= 63 u
63 u = 504
1 u = 504 ÷ 63 = 8
Total number of pencils that they have
= 3 x 36 u
= 108 u
= 108 x 8
= 864
Answer(s): 864
