Vanessa, Opal and Dana have equal number of beads. Vanessa packs all her beads equally into 9 packets. Opal packs all her beads equally into 4 packets. Dana packs all her beads equally into 6 packets. 4 packets of Vanessa's beads, 3 packets of Opal's beads and 5 packets of Dana's beads add up to 438 beads. How many beads do they have altogether?
| |
Vanessa |
Opal |
Dana |
| Number of packets |
9 |
4 |
6 |
| Number of beads |
36 u |
36 u |
36 u |
| Number of beads in each packet |
4 u |
9 u |
6 u |
All the beads can be put into the packets without remainder.
All the children have equal numbers of beads.
Make the number of beads that each child has the same. LCM of 9, 4 and 6 = 36
Number of beads that each child has = 36 u
Number of beads in 1 packet of Vanessa's beads = 36 u ÷ 9 = 4 u
Number of beads in 1 packet of Opal's beads = 36 u ÷ 4 = 9 u
Number of beads in 1 packet of Dana's beads = 36 u ÷ 6 = 6 u
Number of beads in 4 packets of Vanessa's beads, 3 packets of Opal's beads and 5 packets of Dana's beads
= (4 x 4 u) + (3 x 9 u) + (5 x 6 u)
= 16 u + 27 u + 30 u
= 73 u
73 u = 438
1 u = 438 ÷ 73 = 6
Total number of beads that they have
= 3 x 36 u
= 108 u
= 108 x 6
= 648
Answer(s): 648
