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Lemur [1.5K]
3 years ago
13

Salvatore is making party favors for his birthday party. He has 96 pencils and 80 boxes of raisins. Find the GCF of 96 and 80 to

figure out how many party favors he can make. How many pencils and boxes of raisins will be in each one?
Mathematics
2 answers:
goldfiish [28.3K]3 years ago
8 0

The greatest common factor is 18

Then you divide 18 by 96 then 80

80/16=5

96/16=6

So therefore there are 5 boxes of raisins and 6 pencils in each bag

Tema [17]3 years ago
7 0

Answer:

GCF is 16, and 6 pencil boxes, and 6 boxes of raisins.

Step-by-step explanation:

Since, we know the factors of 96 and 80 as:

96 is: 2 x 2 x 2 x 2 x 2 x 3.

85 is: 2 x 2 x 2 x 2 x 5.

So, the factors in common are:

85 and 96: 2 x 2 x 2 x 2

therefore, HCF is:

2 x 2 x 2 x 2 = 16

For pencil boxes,

\frac{96}{16} = 6

For raisins boxes,

\frac{80}{16} = 5

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Vinvika [58]

Answer:

The dimensions that give the minimum surface area are:

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And the minimum surface is:

S = 1,176 cm^2

Step-by-step explanation:

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The surface of this prism is:

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If the base of the prism is a square, then we have L = W

Then the equations become:

V = L*L*H = L^2*H

S = 2*(L^2 + 2*H*L)

We know that the volume of the figure is 2744 cm^3

Then:

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In this equation, we can isolate H.

H = (2744 cm^3)/(L^2)

Now we can replace this on the surface equation:

S = 2*(L^2 + 2*L* (2744 cm^3)/(L^2))

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Now we want to minimize the surface area, then we need to find the zeros of the first derivative of S.

S' = 2*(2*L) - 4*(2744 cm^3)/L^2

This is equal to zero when:

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Then the length of the base that minimizes the surface is L = 14.

Then we have:

H = (2744 cm^3)/(L^2) = (2744 cm^3)/(14cm)^2 = 14cm

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S = 2*(L^2 + 2*L*H) = 2*( (14cm)^2 + 2*(14cm)*(14cm)) = 1,176 cm^2

8 0
2 years ago
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