40 Percent Off Of 39.99

All Algebra ane Resource

A girl in County A spent $75 before a 7.25% sales taxation and a daughter in Canton B spent $seventy before an 8% sales tax. How much more money did the daughter from County A spend than the girl from County B afterwards sales tax was practical? Round to the nearest hundredth.

Possible Answers:

$ii.63

$1.63

$4.84

$5.84

$xvi.25

Caption:

Canton A: Multiply the price by the sales tax to notice out how much coin the sales revenue enhancement will add. Retrieve to convert per centum to decimal!

$75 * 0.0725 = $5.4375

Add the original price and the sales tax.

$75 + $5.4375 = $80.4375

County B: Multiply the price past the sales tax to find out how much coin the sales tax volition add. Retrieve to convert pct to decimal!

$70 * 0.08 = $5.6

Add the original cost and the sales tax.

$seventy + $5.6 = $75.half dozen

And then take the difference.

80.4375 – 75.6 = four.8375

Round to the nearest hundredth: $4.84

Mary was shopping for a new wearing apparel, and institute ane she liked for $48. Better however, it was 25% off. How much did Mary pay for the wearing apparel?

Caption:

To find the auction price we can set upwards a proportion. 25/100 = ten/48. We keep the 100 and 48 both on the bottom of the fraction since they represent the "whole". x represents the discount off the full price of the clothes. To solve this proportion, we cross multiply, yielding 48 * 25 = 100x. Alternatively, if you observe that 25/100 simplifies to 1/iv, we tin use 1/four in our proportion instead of 25/100, thus, 1/4 = x/48. Then, cross multiplying, we go 48 = 4x, so x = 12. Then nosotros subtract this discount from the original cost yielding 48 – 12 = 36; thus, she paid $36 for the dress.

25% = 25/100

$\frac{25}{100}=\frac{x}{48}$

$\frac{1}{4}=\frac{x}{48}$

(1) * (48) = (iv) * (x)

48 = 4x

(48)/4 = (4x)/4

12 = x

The discount is $12.

$48 – $12 = $36

Robin sees that a jacket at the mall has been marked down xx% from an original price of $49.99. Taking into business relationship the sales tax of 8%, which is practical after taking the discount, how much will Robin have left over if she brought $60 to the mall?

Correct answer:

$\$16.81$

Explanation:

Afterward the discount, she volition pay for the remaining cost of the jacket. This price will be equal to the pct remaining later the disbelieve.

100% – xx% = 80%

She will pay for 80% of the original toll.

80% = 0.80

$\$49.99 * (0.80) = \$39.99$

Add in the sales taxation.

8% = 0.08

$\$39.99+ (\$39.99*0.08) = \$39.99+ (\$3.20)=\$43.19$

Decrease the concluding price from Robin'due south budget of $60.

$\$60.00 - \$43.19 = \$16.81$

There is a sale for twenty% off on a sweater your grandma wants to buy you for christmas. The original toll is $fifteen.98. How much does the sweater cost with the discount?

Correct respond:

$\$12.79$

Caption:

To notice the answer, yous must beginning convert the sales pct to a decimal by moving the decimal left 2 places.

$20\% =0.20$

So, multiply the total price by the decimal.

$\$15.98(0.20)=\$3.19$

This gives the states the amount of the discount. To find the remaining price, nosotros subtract that number from the original cost to get the answer.

$\$15.98-\$3.19=\$12.79$

A shirt that originally cost $45 is on sale. The auction price is fifteen% off of the original price. What is the auction toll?

Correct answer:

$\$38.25$

Explanation:

First, summate 15% of $45:

$\small 0.15\times 45 = 6.75$

Therefore, the disbelieve is $half-dozen.75 off of the price of the shirt. To discover the sale cost, subtract the discount from the original price:

$\small 45-6.75=38.25$

An detail is marked upwards by 25% and and then marked down by 40%. What pct of the original cost is the new price?

Correct respond:

$75\%$

Explanation:

The quickest way to do this problem is to realize that a "mark upwards" is washed by adding that percentage to 100%. For instance a forty% markup is performed by multiplying by 1.four. A markdown is done by subtracting that percentage from 100%. For instance, a 25% markdown is performed past multiplying past 0.75. (Recall of the latter case like this: it is 75% of its original price.)

Based on these remarks, the problem is easy. While we practise not know our toll we know that the first markup gives us:

1.25 * x

To this, nosotros now perform the mark down:

0.6 * 1.25 * x

Multiply out your coefficients (the numbers in the front):

0.75 * x

This is the aforementioned thing as proverb "75% of the original price ()."

The price of an item is $xviii afterward a 25% discount. What was its original price?

Correct answer:

$\$24$

Caption:

If something is discounted $25\%$ , it is really $75\%$ of its original price. The question is thus asking, " $75\%$ of what is $\$18$ ?" This tin exist translated every bit:

0.75 * x = 18

Solve for by dividing both sides of the equation past 0.75 :

$\frac{0.75*x}{0.75} = \frac{18}{0.75}$

x=24

Therefore, it was originally $\$24$ .

The price of an item is $25 after a 60% discount. What was the original price?

Correct answer:

$\$62.50$

Caption:

When an particular is marked down $60\%$ , it is $40\%$ of its original toll. The question could be rephrased as " $40\%$ of what is $\$25$ ?" This could exist rewritten equally an equation rather but:

0.40 * x = 25

Solve forten by dividing both sides past 0.forty:

$x = \frac{25}{0.40} = 62.5$ .

At a department shop, a high-finish pair of jeans normally costs $170. This week, the store is having a auction and marked the jeans 20% off. However, Jane is an employee of the store and gets an additional 25% discount off the already discounted sale price. How much will Jane pay for the jeans?

Correct answer:

$\$102$

Explanation:

The first step is to find 20% of $170. This can be washed easily by multiplying 170 by 0.2, yielding $34. Nosotros subtract 34 from 170 to get the initial sale price, $136. Next, nosotros have to take 25% of that already discounted figure, and we do this by multiplying 136 by 0.25. Once more, we happen to become $34, and after we subtract that number from 136 we get our last toll, $102. The other reply choices are either the issue of forgetting a step or of simple calculation errors.

Mr. Jones is trying to restrict his expenditures on groceries to 12% of his bacon. He makes $756.00 weekly, and he lives in a land where the sales tax rate is 6.125% on groceries. Calculate the maximum pricebefore sales tax of the groceries Mr. Jones can buy each calendar week in order to stick to his self-imposed limit.

Correct answer:

$\$85.48$

Explanation:

According to his rule, Mr. Jones can spend 12% of $756.00 weekly.

$0.12* \$756.00 = \$90.72$

This is the amount he tin can spend afterwards sales tax.

Permit be the price of the groceriesbefore the sales tax is figured in.

The sales revenue enhancement paid is 6.125% of , or 0.06125x , so the amount paid for the groceries is x+ 0.06125x= 1.06125x .

Since Mr. Jones is limited to spending $xc.72, this ways that $1.06125x \leq 90.72$ . We can solve the inequality for .

$x \leq \$90.72 \div1.06125$

$x\leq \$85.48$

The maximum amount Mr. Jones tin spend earlier tax is $85.48.

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