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Law Incorporation [45]
3 years ago
15

A store offers a 15% discount on all items in the store during a sale. All store employees get an additional 10% employee discou

nt. In the equation below,
C represents the cost of an item for an employee including tax and x represents the original price of the item:

C = 0.765x + 0.06(0.765x)

Chris is an employee at the store. He plans to buy a coat during the sale. The price of the coat before the discount is $100. How much will Chris pay for the coat during the sale?
Mathematics
1 answer:
Leona [35]3 years ago
3 0
<span>x = 100

Plug in your equation, C.

C = 0.765(100) + 0.06[0.765(100)]
C = 76.5 + 0.06(76.5)
C = 76.5 + 4.59
C = 81.09

After the discount, Chris will pay $81.09 for the coat. </span>
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A man travels 20 km by car from Town P to Town Q at an average speed of x km/h. He finds that the time of the journey would be s
yuradex [85]

Answer:

x = 20.

Step-by-step explanation:

First, you should remember the relation:

Distance = Speed*Time.

First, we know that a man travels a distance of 20km at a speed of x km/h, in a time T.

We can write this as:

20km = (x km/h)*T

We know that the time is shortened by 12 minutes if the speed is increased by 5km/h

Rewriting these 12 minutes in hours (remember that 60min = 1 hour)

12 min = (12/60) hours = 0.2 hours

Then from this, he can travel the same distance of 20km in a time T minus 0.2 hours if the speed is increased by 5 km/h

We can write this as:

20km = (x + 5 km/h)*(T - 0.2 h)

Then we have a system of two equations, and we want to find the value of x:

20km = (x km/h)*T

20km = (x + 5 km/h)*(T - 0.2 h)

First, we should isolate the variable T in one of the equations, if we isolate it in the first one, we will get:

20km/(x km/h) = T

Replacing that in the other equation we get:

20km = (x + 5 km/h)*(T - 0.2 h)

20km = (x + 5 km/h)*( 20km/(x km/h) - 0.2 h)

Now we can solve this for x.

Removing the units (that we know that are correct) so the math is easier to read, we get:

20 = (x + 5)*(20/x - 0.2)

We only want to solve this for x.

20 = x*20/x - x*0.2 + 5*20/x - 5*0.2

20 = 20 - 0.2*x + 100/x - 1

subtracting 20 in both sides we get:

20 - 20 = 20 - 0.2*x + 100/x - 1 - 20

0 = -0.2*x + 100/x - 1

If we multiply both sides by x we get:

0 = -0.2*x^2 + 100 - x

-0.2*x^2 - x + 100 = 0

This is just a quadratic equation, we can solve it using the Bhaskara's equation, the solutions are:

x = \frac{-(-1) \pm \sqrt{(-1)^2 - 4*(-0.2)*100} }{2*-0.2}  = \frac{1 \pm 9 }{-0.4}

Then the two solutions are:

x = (1 + 9)/-0.4 = -25

x = (1 - 9)/-0.4 = 20

As x is used to represent a speed, the negative solution does not make sense, so we should use the positive one.

x = 20

then the average speed initially is 20 km/h

3 0
2 years ago
The quotient of two numbers is -12. One of the numbers is −3. What is the other number?
umka21 [38]
The answer is -4 because -4 times -3 equals -12
6 0
3 years ago
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ipn [44]

Answer:

Step-by-step explanation:

perimeter of rectangle=2(length+width)

=2(70+65)

=2*135

=270 feet

4 0
3 years ago
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The price of an item has been reduced by $8.39 . The new sale price is $51.23. What was the original price?
Karolina [17]

Answer:59.62

Step-by-step explanation:

0riginal price=selling price+discount

=51.23+8.39

=59.62

6 0
3 years ago
What is the volume of the figure below if a = 4.5 units, b = 5.8 units, and c = 3 units?
Anastasy [175]

Answer:

The answer to your question is the letter C

Step-by-step explanation:

Data

a = 4.5 u

b = 5.8 u

c = 3 u

Process

1.- Calculate the volume of the rectangular prisms

Formula

Volume = a x a x c

Substitution

Volume = 4.5 x 4.5 x 3

Result

Volume = 60.75 u³

But there are two rectangular prism

Total volume = 2 x 60.75

                      = 121.5 u³

2.- Calculate the volume of the triangles

Formula

Volume = base x width x height

Substitution

Volume = 5.8 x 3 x 4.5

Result

Volume = 78.3 u³

3.- Total volume

Volume = 121.5 + 78.3

             = 199.8 u³

3 0
3 years ago
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