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Marina CMI [18]
2 years ago
5

a sign says that the price marked on all music equipment is 30% off the original price you buy an electric guitar for sale price

of $315 what is the original price
Mathematics
1 answer:
prohojiy [21]2 years ago
5 0

The original price is $450.

<u>Step-by-step explanation:</u>

Step 1:

Given details, Discount%, D% = 30 and Selling Price, SP = $315

Step 2:

Write down formula for calculating the Original Price

Selling Price (SP) = Original Price (OP) - Discount (D)

Discount (D) = Original Price (OP) * (D%/100)

Step 3:

Substitute given values in the formula

315 = OP - D

D = OP \times30/100

D = 0.3 OP

Step 4:

Substitute value of D in the first formula

315 = OP - 0.3 OP

315 = OP (1 - 0.3) = 0.7 OP

Original Price, OP = 315/0.7 = $450

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A sports company wants to package a ball with a 1.5-inch radius in sets of two. They have two options: a cylinder or a square pr
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Step 1

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we know that

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In this problem we have

r=1.5\ in

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V=\frac{4}{3} \pi 1.5^{3}=4.5\pi\ in^{3}

so

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Step 2

Find the volume of a cylinder

we know that

The Volume of a cylinder is equal to    

V=\pi r^{2}h

In this problem we have

r=1.5\ in

h=4*r=4*1.5=6\ in    

Substitute

V=\pi (1.5^{2})(6)=13.5 \pi\ in^{3}

Step 3

Find the amount of wasted space in the cylinder

Subtract the volume of the two balls from the volume of the cylinder

13.5\pi\ in^{3}-9\pi\ in^{3}=4.5\pi\ in^{3}=14.14\ in^{3}    

Step 4

Find the volume of the square prism

The volume of the prism is equal to

V=Bh

where

B is the area of the base of the prism

h is the height of the prism

In this problem we have

B=(2*1.5)^{2}=9\ in^{2} -----> the base is equal to the diameter    

h=4*r=4*1.5=6\ in  

Substitute

V=9*6=54\ in^{3}

Step 5

Find the amount of wasted space in the prism

Subtract the volume of the two balls from the volume of the prism

54\ in^{3}-9\pi\ in^{3}=25.73\ in^{3}  

Step 6

Compare the amount of wasted space

the amount of wasted space in the cylinder is 14.14\ in^{3}

the amount of wasted space in the prism is  25.73\ in^{3}

Find the difference

25.73\ in^{3}-14.14\ in^{3}=11.59\ in^{3}=11.6\ in^{3}

The package that has the least amount of wasted space is the cylinder

therefore

<u>the answer is the option</u>

the cylinder because it has approximately 11.6 in.3 less wasted space than the prism

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