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Alona [7]
3 years ago
8

Mara bought 8 boxes of pencils and 3 packages of pens for $24. At the same store, Elaine bought 4 boxes of pencils and 6 package

s of pens for $30. How much does one box of pencils cost
Mathematics
1 answer:
drek231 [11]3 years ago
4 0

Answer:

pencils=$4

pen=$1.5

Step-by-step explanation:

Step one:

given data

let pencils be x and pens be y

Mara bought 8 boxes of pencils and 3 packages of pens for $24

8x+3y=24------------1

Elaine bought 4 boxes of pencils and 6 packages of pens for $30

4x+6y=30------------2

solve 1 and 2 simulteneoulsy

8x+3y=24---------X1

4x+6y=30----------X2

subtract the answer bellow

8x+3y=24

8x+12y=60

0-9y=-36

divide both sides by- 9

y=36/9

y=$4

put y= 4 in 1

8x+3*4=24

8x+12=24

8x=24-12

8x=12

divide both side by 8

x= 12/8

x=3/2

x= $1.5

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Answer:

QUESTION 2:

The area of the polygon is 21.5 units²

QUESTION 3:

The area of the combined figure is 12 + 18.25·π units²

QUESTION 4:

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The area of the compost shape is 40 in.²

Step-by-step explanation:

QUESTION 2.

The area of the polygon is given as follows;

The area of two triangles + The area of trapezoid

1/2×6×3 + 1/2×3×4 + 1/2×(6 + 7) = 21.5 units²

QUESTION 3

The diameter of the semicircle, 'd', is given as follows;

d = √(8² + 3²) = √73

The area of the semicircle = π·d²/4 = π·73/4 = 18.25·π unit²

The area of the right triangle beside the semicircle is given as follows;

1/2 × 8 × 3 = 12 unit²

The area of the combined figure = The area of the semicircle + The area of the right triangle

∴ The area of the combined figure = 12 + 18.25·π units²

QUESTION 4:

The dimensions of the parallelogram are;

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Length, L = √(8² + 2²) = √(68)

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The area of the parallelogram, A_R = 34 units²

The length of a parallel side, 'A', of the parallelogram is A = 6

The height of the parallelogram, is h = 1

The area of the parallelogram is A = B·h = 6 × 1 = 6 units²

The area of the figure is the sum of the area of the rectangle and the area of the parallelogram

Therefore, we have;

The area of the figure = 34 units² + 6 units² = 40 units²

QUESTION 5

The composite shape consists of a triangle and a rectangle

Therefore, we have;

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The area of the triangle = 1/2 × 2 in. × 5 in. = 5 in.²

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5 0
3 years ago
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Juliette [100K]

Answer:

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Step-by-step explanation:

When doing these types of problems, the main goal is to get the variable by itself. Its kind of hard to explain with words so I will just use numbers.

15x + 14 = 149

(Subtract 14 on both sides. Remember, when you do something (Like subtracting, adding, etc.) on one side you have to do it to the other.)

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---------------------------

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(Divide 15 on both sides. Since we need to use inverse operation to cancel the 15 out, we would divide 15 on both sides.)

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