An egg farm packages 264 total cartons of eggs each month. The Farm has 3 different sizes of cartons. The samalln cartons holds 8 eggs & 1/6 of the total cartons are small. The medium carton holds 12 eggs & 2/3 of the total cartons are medium. The large carton holds 18 eggs & the rest of the total cartons are large. Determine how many of each size carton is needed each month. Then determine how many eggs are needed to fill the 264 cartons. Answer solve explain & show your work

1/6 * 264 = 44 small cartons
2/3 * 264 = 174 medium cartons

1/6 + 2/3 = 5/6, so there is 1/6 left for the large cartons , since the fractions
must add up to 1

1/6 * 264 = 44 large cartons

44*8 + 174*12 + 44*18 = 3232 eggs are needed to fill the 264 cartons

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astha8579 astha8579 · Answer 2 · 2022-04-15T13:10:21+02:00

Each month, we need 44 smaller cartons, 176 medium cartons and 44 larger cartons. The number of eggs that are needed to fill the 264 cartons is 3,256

How to find the one-nth part of a thing?

Suppose that the whole thing is of value V.

Then its one-nth part is symbolically written as:

[tex]V \times \dfrac{1}{n}[/tex]

(V is divided in n equal part, and each part is called one-nth part of V).

We're specified that:

Farm has 3 different sizes of cartons.
Total cartons = 264
Smaller carton holds 8 eggs.
number of smaller cartons = 1/6th of total carton
Medium carton holds 12 eggs.
number of medium cartons = 2/3th of total carton
Large carton holds 18 eggs.
number of large cartons = rest of total carton

Number of smaller cartons = 1/6th of total cartons (which is 264) = [tex]264 \times \dfrac{1}{6} = 44[/tex]
Number of medium cartons = [tex]264 \times \dfrac{2}{3} = 176[/tex]

Number of larger cartons = 264 - number of smaller and medium cartons

= 264 - (44 + 176) = 264 - 220 = 44

Thus, each month, we need 44 smaller cartons, 176 medium cartons and 44 larger cartons.

The number of eggs needed to fill 44 smaller cartons = [tex]8 \times 44 = 352[/tex]

The number of eggs needed to fill 176 medium cartons = [tex]12 \times 176= 2112[/tex]

The number of eggs needed to fill 44 larger cartons = [tex]18 \times 44 = 792[/tex]

(multiplied number of eggs' capacity of each type of box to the number of boxes of each type).

Thus, the number of eggs that are needed to fill the 264 cartons is = 352 + 2112+ 792 = 3,256

Thus, each month, we need 44 smaller cartons, 176 medium cartons and 44 larger cartons. The number of eggs that are needed to fill the 264 cartons is 3,256

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