Question

Jade has 121,024 beads. 1/5 of them are glass beads, 1/10 of them are pony beads, and the rest of them are marbled beads. It takes 20 glass beads, 50 marbled beads, and 30 pony beads to make a necklace. How many necklaces can Jade make?

Answer 1

Jade can make 403 necklaces.

1/5 of 121024 = 1/5(121024) = 0.2(121024) = 24204.8 = 24204 glass beads
1/10 of 121024 = 1/10(121024) = 0.1(121024) = 12102.4 = 12102 pony beads

To find the number of marbled beads, we add the fraction of the other two kinds together:
1/5 + 1/10

We will use 10 as the denominator:
2/10 + 1/10 = 3/10

The fraction that the marbled beads represents will make up 100%, or the whole number 1:
1-3/10 = 7/10

7/10 of 121024 = 7/10(121024) = 0.7(121024) = 84716.8 = 84716 marbled beads

Since it takes 20 glass beads to make a necklace, we divide the number of glass beads, 24204, by 20:
24204/20 = 1210 necklaces

It takes 30 pony beads to make a necklace.  We divide the number of pony beads, 12102, by 30:
12102/30 = 403 necklaces

It takes 50 marbled beads to make a necklace.  We divide the number of marbled beads, 84716, by 50:
84716/50 = 1694 necklaces

We must go with the smallest number, in order to ensure we have enough beads; this means she can make 403 necklaces.