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Simora [160]
3 years ago
15

The sum of two books and a pencil is $6.00. The difference of cost between 3 books and 2 pencils is $ 2.00. Find the cost of a b

ook and a pencil.​
Mathematics
1 answer:
Gala2k [10]3 years ago
8 0

Answer:

The book costs $2 and the pencil also costs $2.

Step-by-step explanation:

It is easy to get the value of the book and the pencil if we use<em> algebraic expressions.</em>

Let x be the cost of the book and let y be the cost of the pencil.

The sum of 2 books and a pencil is $6.00

  • 2x + y = $6.00

The difference of cost between 3 books and 2 pencils is $2.00.

  • 3x - 2y = $2.00

Step 1: Let's get the value of y first.

2x + y = 6

y = 6 - 2x

Step 2: Let's substitute the value of y and look for the value of x.

3x - 2y = $2.00

3x - 2(6-2x) = 2

3x - 12 + 4x = 2

7x = 12 + 2

7x = 14

x = \frac{14}{7}

x = $2 (this is the cost of the book)

Step 3: Let's substitute the value of x and look for the value of y.

2x + y = 6

2 (2) + y = 6

4 + y = 6

y = 6 - 4

y = $2 (this is the cost of the pencil)

Let's check:

2x + y = $6

2(2) + 2 = 6

4 + 2 = 6

6 = 6<em> (CORRECT)</em>

<em></em>

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Answer:

The image in the attached figure

Step-by-step explanation:

we know that

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In this problem the scale factor is 1/4

The height of the pre-image is 4 units

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Find out the dimensions of the image

The height of the image is (4)\frac{1}{4}=1\ unit

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The image in the attached figure

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Josiah invests $360 into an account that accrues 3% interest annually. Assuming no deposits or withdrawals are made, which equat
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Hope this helps! :)
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2 years ago
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The circumference of Tyler's bike tire is 72 inches. What is the diameter of the tire?​
pantera1 [17]

Answer:

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Step-by-step explanation:

Hello, I can help you with this question

in this case we know the circumference of a circle, and we need to find out the diameter.

let's remember

the radius of a circle can be defined as

radius=\frac{diameter}{2}\\ or\\diameter=2* radius( equation\ 1)\\

also

circumference=2*\pi  *radius(equation2)\\

Step1

replace the value of the circumference of tyler's bike in equation 2  and isolate radius to find radius

72 inches=2*\pi  *radius\\\\radius=\frac{72}{2*\pi  } \radius =11.46\ inches

Step 2

now, replace the value of radius into equation 1 to find diameter

radius=11.46 in

diameter=2* radius( equation\ 1)\\\\diameter=2*11.46\\diameter=22.92

so, the diameter is 22.92 inches

I really hope it helps, have a great day.

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