Question

Solve.

17. A jewelry maker will use 24 jade beads and 30 teak beads to make
necklaces. Each necklace will have the same numbers of jade beads
and teak beads. What is the greatest number of necklaces she can
make? How many beads of each type are on each necklace?​

Answer 1

• The greatest number of necklaces she can make is:
  `6`
• There are 4 jade beads and 5 teak beads on each necklace.

Explanation:

In order to calculate the greatest number of necklaces she can make, you must find the Greatest Common Factor (GCF) between 24 and 30.

Descompose 24 and 30 into their prime factors:

`24=2*2*2*3=2^3*3\\\\30=2*3*5`

Multiply the commons with the lowest exponents:

`GCF=2*3\\\\GCF=6`

The greatest number of necklaces she can make is:
`6`

Let be "j" the number of jade beads on each necklace and "t" the number of teak beads on each necklace.

Dividing the number of jade beads and the number of teak beads she will use by the GCF, you get:

`j=(24)/(6)=4\\\\t=(30)/(6)=5`