a jewelry is designing a crown. the crown must have at least 45 gems using only emeralds, rubies, and diamonds. the number of rubies must be 1 less than 3 times the number of emeralds. the number of diamonds must be 4 or less than the number of rubies. which inequality could the jewelry maker use to find the number of emeralds, x, that can be placed on the crown>

I'm horrible at this so I'm just guessing.
X is the variable and x means multiplication symbol.
X + (X x 3 - 1) + (X x 3 - 1) - 4) ≥ 45 is the answer I got.
The answer to that inequality would be
X ≥ 7 I think.

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facundo3141592 facundo3141592 · Answer 2 · 2021-12-02T05:34:38-05:00

We want to write an inequality to see how many emeralds can be placed on the crown. The inequality is E ≥ 8

We know that the crown must have, at least, 45 gems.

The jewelry will use:

D = number of diamonds
E = number of emeralds
R = number of rubies.

Then we must have:

D + E + R ≥ 45

We also know that:

R = 3E - 1

D = R - 4

We want to solve it for E, the number of emeralds, then we rewrite the second equation as:

D = R - 4 = ( 3E - 1) - 4

D = 3E - 5

Now we can replace these two relations in the inequality to get:

D + E + R ≥ 45

(3E - 5) + E + (3E - 1) ≥ 45

7E - 6 ≥ 45

7*E ≥ 45 + 6

E ≥ 51/7 = 7.3

Rounding to the next whole number (because 7.3 of an emerald makes no sense) we get:

E ≥ 8

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