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2 years ago

If a pair of shoes costs $52.50 including a 7.25% tax, what is the original cost of the item before taxes are added?

Mathematics

1 answer:

enot [183]2 years ago

4 0

Answer:

The original cost of the pair of shoes before tax is $48.95

Step-by-step explanation:

* Lets explain how to solve the problem

- Assume that the cost of the pair of shoes is 100% before taxes

∵ The cost of the pair of shoes is 100% before taxes

∵ The tax is 7.25%

∴ The price of the pair of shoes after tax = 100% + 7.25% = 107.25%

- This 107.25% equivalent to the price of the pair of shoes including

the tax

∵ The cost of the pair of shoes including tax is $52.50

- Lets use the cross multiplication to find the cost of the pair of

shoes before tax

∵ 100% ⇒ 107.25%

? ⇒ 52.50

- ? represents the cost of the pair of shoes before tax

∴ ? = $\frac{100*52.50}{107.25}=48.95$

∴ The original cost of the pair of shoes before tax is $48.95

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2 years ago

Read 2 more answers

A batter strikes a baseball. the equation y = -0.005^2 +0.7x + 3.5 models its path, where x is the horizontal distance, in feet,

hram777 [196]

Answer:

(D)144.8 feet

Step-by-step explanation:

Given the equation which models the path of the baseball

$y = -0.005x^2 +0.7x + 3.5$

where x is the horizontal distance, in feet, the ball travels and y is the height, in feet, of the ball.

To determine how far from the batter the ball will land, we determine the distance x at which the height, y=0.

$y = -0.005x^2 +0.7x + 3.5=0$

$-0.005x^2 +0.7x + 3.5=0$

We use the quadratic formula to solve.

In the quadratic equation above, a=-0.005, b=0.7, c=3.5

$x=\dfrac{-b\pm\sqrt{b^2-4ac} }{2a} \\=\dfrac{-0.7\pm\sqrt{0.7^2-4(-0.005*3.5)} }{2*-0.005} \\=\dfrac{-0.7\pm\sqrt{0.49+0.07} }{-0.01}\\=\dfrac{-0.7\pm\sqrt{0.56} }{-0.01}\\x=\dfrac{-0.7+\sqrt{0.56} }{-0.01} \: or\: x=\dfrac{-0.7-\sqrt{0.56} }{-0.01}\\x=-4.83 \: or\: x=144.83$

Since x cannot be negative, x=144.8 feet to the nearest tenth of a foot.

The correct option is D.

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