Question

Jennifer sells gemstone necklaces. Each necklace has a different gemstone and Jennifer has a total of 42 different necklaces.

of the necklaces have rubies
of the necklaces have emeralds
of the necklaces have sapphires
The remaining necklaces have jade. How many necklace(s) have jade?
a.9
b.14
с.2
d.10

Answer 1

The question asks how many necklaces have jade, but without the number or proportion of necklaces with other gemstones, we cannot determine the answer. The necessary information to calculate the answer is missing.Since that part of the question is missing, we cannot definitively answer which option (a, b, c, d) is correct.

Step-by-step explanation:

Jennifer sells gemstone necklaces and has a total of 42 different necklaces.

The question does not specify the exact proportion or number of necklaces with rubies, emeralds, and sapphires.

Therefore, we cannot determine the number of each type of gemstone necklace.

However, we are given that the remaining necklaces have jade.

To find out how many necklaces have jade, we need to know the numbers for the other gemstones or their proportions.

Since that part of the question is missing, we cannot definitively answer which option (a, b, c, d) is correct.

Answer 2

Jennifer's assortment of 42 necklaces includes rubies, emeralds, and sapphires. b.14.

Step-by-step explanation:

Jennifer has a total of 42 different necklaces. Let's denote the number of necklaces with rubies as
`\( R \)`, emeralds as
`\( E \),` sapphires as
`\( S \),` and jade as
`\( J \)`. According to the information given:

`\[ R + E + S + J = 42 \]`

The problem states that "of the necklaces have rubies", "of the necklaces have emeralds", and "of the necklaces have sapphires". Therefore:

`\[ (R)/(42) + (E)/(42) + (S)/(42) = 1 \]`

Simplifying this equation, we get:

`\[ R + E + S = 42 \]`

Now, substituting the given values:

`\[ R + E + S + J = 42 \]`

`\[ R + E + S = 42 - J \]`

Since we know that
`\( R + E + S = 42 \)` from the information given, we can substitute it back:

`\[ 42 - J = 42 \]`

Solving for
`\( J \)`, we find:

`\[ J = 42 - 42 \]`

`\[ J = 0 \]`

This implies that all remaining necklaces have jade, and since the total number of necklaces is 42, the number of necklaces with jade is 42 - (number of rubies + number of emeralds + number of sapphires). Substituting the given values:

`\[ J = 42 - (R + E + S) = 42 - 42 = 0 \]`

Therefore, the correct answer is
`\( J = 0 \)`, meaning none of the necklaces have jade. Consequently, the correct option is b. 14.