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stepladder [879]

3 years ago

15

A fruit company delivers its fruit in two types of boxes: large and small. a delivery of 6 large boxes and 5 small boxes has a t

otal weight of 127 kilograms. a delivery of 2 large boxes and 3 small boxes has a total weight of 51 kilograms. how much does each type of box weigh?

1 answer:

Afina-wow [57]3 years ago

5 0

6 large + 5 small = 127 kg ------------ (1)
2 large + 3 small = 51kg ------------ (2)

<u>(2) x 3 :</u>
6 large + 9 small = 153 ---------------- (2a)

<u>(2a) - (1) :</u>
4 small = 26
1 small = 6.5kg ------------ (sub into equation 1)

6 large + 5 small = 127 kg
6 large + 5(6.5) = 127
6 large + 32.5 = 127
6 large = 127 - 32.5
6 large = 94.5
1 large = 15.75 kg

Answer: The small box weighs 6.5kg and the big box weighs 15.75 kg

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4 years ago

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Juan is three times as old as Gabe and Gabe is six years older than Catherine. If the sum of their ages is 149, how old is each

cestrela7 [59]

Answer:

Juan = 93 years.

Gabe = 31 years.

Catherine = 25 years.

Step-by-step explanation:

Let the age of Juan = J

Let the age of Gabe = G

Let the age of Catherine = C

<em>Translating the word problem into an algebraic equation, we have;</em>

$J = 3G$ ..........equation 1

$G = C + 6$ ........equation 2

$J + G + C = 149$ ........equation 3

<em>We would solve the linear equations by using the substitution method; </em>

<em>Substituting equation 2 into equation 1;</em>

$J = 3(C + 6)$

$J = 3C + 18$ ........equation 4

<em>Substituting equation 2 and equation 4 into equation 3;</em>

$(3C + 18) + (C + 6) + C = 149$

<em>Simplifying the equation, we have;</em>

$5C + 24 = 149$

$5C = 149 - 24$

$5C = 125$

$C = \frac {125}{5}$

C = 25 years.

To find G; from equation 2

$G = C + 6$

Substituting the value of "C" into equation 2, we have;

$G = 25 + 6$

G = 31 years.

To find J; from equation 1

$J = 3G$

Substituting the value of "G" into equation 1, we have;

$J = 3 * 31$

J = 93 years.

<em>Therefore, Juan is 93 years old, Gabe is 31 years old and Catherine is 25 years old. </em>

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3 years ago

Wesly reads 60 pages in 20 minutes if he reads at the same constant rate what equation could represent this as a proportional re

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Answer:

let m be minutes, p be pages

pages read = times(in minutes) * reading speed(pages per minutes)

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p=3m

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3 years ago

A house number is displayed on a plaque in the shape of a regular 7-sided polygon. The area of the plaque is 70 squared inches.

Svetllana [295]

Answer:

The perimeter of the plaque is 28 inches.

Step-by-step explanation:

Given : A house number is displayed on a plaque in the shape of a regular 7-sided polygon. The area of the plaque is 70 squared inches. The perpendicular distance from a side to the center is 5 inches to the nearest inch.

To find : What is the perimeter of the plaque?

Solution :

The 7-sided polygon can be divided into seven triangles whose height, h is equal to the perpendicular distance from each side to the center.

The base of each triangle is equal to the length of a side, s.

The area of each triangle is $A=\frac{1}{2}\times s\times h$

The area of the whole polygon is $A_p=\frac{1}{2}\times 7s\times h$

Now, the perimeter of a regular 7-sided polygon is $P=7s$ .

Substitute in area,

$A_p=\frac{1}{2}\times P\times h$

We have given, $A_p=70\ in^2 and h=5\ in$

$70=\frac{1}{2}\times P\times 5$

$P=\frac{70\times 2}{5}$

$P=28$

The perimeter of the plaque is 28 inches.

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4 years ago

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Lets look at the steps to construct

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Take more distance than half of AC.
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3 years ago

Read 2 more answers