ACT Math : ACT Math

Study concepts, example questions & explanations for ACT Math

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Example Questions

Example Question #1291 : Act Math

How much do you save if you bought a shirt that normally costs 19.99 at a 25% discount? Ignore sales tax and round your answer to the nearest cent.

Possible Answers:

\(\displaystyle \$15.01\)

\(\displaystyle \$4.99\)

\(\displaystyle \$5\)

\(\displaystyle \$25\)

\(\displaystyle \$15\)

Correct answer:

\(\displaystyle \$5\)

Explanation:

To find how much money you save on a sale. Turn the sale percentage into a decimal and multiply it by the normal price:
\(\displaystyle \$19.99*.25 = \$4.9975 = \$5\)

Example Question #21 : Sale Prices

Denzel is going to the store to buy a guitar. He sees one he likes that's listed at \(\displaystyle \$79.99\) but on sale for \(\displaystyle 20\%\) off. How much will Denzel pay if he chooses to buy the guitar (ignore sales tax, round to the nearest cent)?

Possible Answers:

\(\displaystyle \$16.00\)

\(\displaystyle \$99.99\)

\(\displaystyle \$63.99\)

\(\displaystyle \$59.99\)

\(\displaystyle \$65.99\)

Correct answer:

\(\displaystyle \$63.99\)

Explanation:

To find the sales price of an item given that it is \(\displaystyle 20\%\) off, first subtract \(\displaystyle 20\%\) from \(\displaystyle 100\%\). This gives \(\displaystyle 80\%\), which means Denzel is paying for \(\displaystyle 80\%\) of the guitar's original price. Next, convert that into a decimal and multiply by the guitar's cost:

\(\displaystyle 80\% \rightarrow .8 \rightarrow .8*79.99 = 63.992 \rightarrow \$63.99\)

Example Question #21 : How To Find The Sale Price

Julie only has \(\displaystyle \$49.99\)to spend on a prom dress on tax free weekend.  She has narrowed her search down to her four favorites:  a red dress costing \(\displaystyle \$59.99\) but marked down \(\displaystyle 15\%\) a blue dress costing \(\displaystyle \$55.99\) marked down \(\displaystyle 10\%\), a yellow dress costing \(\displaystyle \$65.99\) marked down \(\displaystyle 25\%\), and a purple dress costing \(\displaystyle \$75.99\) marked down \(\displaystyle 30\%\).  Which dress can Julie buy?  

Possible Answers:

blue dress

red dress

She cannot afford any of the dresses.  

purple dress

yellow dress

Correct answer:

yellow dress

Explanation:

This is a percentages problem.  To find the price of an item on sale by a certain percentage, you subtract that percentage decimal from 1.0, and multiply that number by the cost of the dress. Then, you compare that number to the amount she has to see if she can afford it. 

Red dress price= \(\displaystyle \$59.99*(1-0.15)=\$59.99 * 0.85 = \$50.99 >\; \$49.99.\)

Blue dress price= \(\displaystyle \$55.99*(1-0.0.10)=\$55.99 * 0.90 = \$50.39 >\; \$49.99.\)

Yellow dress price= \(\displaystyle \$65.99*(1-0.25)=\$65.99 * 0.75 = \$49.49 < \; \$49.99.\)

Purple dress price= \(\displaystyle \$75.99*(1-0.30)=\$75.99 * 0.70 = \$53.19 >\; \$49.99.\)

Since the yellow dress is the only dress under her total amount of money, that is the only dress she can afford.  

Example Question #21 : Sale Prices

To find the sale price for a single item or group of like items, one can use the equation \(\displaystyle P_d = P_o(1-S)\), where \(\displaystyle P_d\) is the discounted price, \(\displaystyle P_o\) is the original price, and \(\displaystyle S\) is the percent to be discounted in decimal form.

A pair of headphones normally sells for \(\displaystyle \$ 70\). If the headphones are on a \(\displaystyle 20 \%\)-off discount, how expensive are they?

Possible Answers:

\(\displaystyle \$56\)

\(\displaystyle \$48\)

\(\displaystyle \$22\)

\(\displaystyle \$50\)

\(\displaystyle \$14\)

Correct answer:

\(\displaystyle \$56\)

Explanation:

To find the new sale price, apply the discount to the original price in decimal form.

\(\displaystyle P_d = P_o(1-S)\) ---> \(\displaystyle P_d = \$70(1-.2) = \$70(.8) = \$56\)

Example Question #24 : Sale Prices

To find the sale price for a single item or group of like items, one can use the equation \(\displaystyle P_d = P_o(1-S)\), where \(\displaystyle P_d\) is the discounted price, \(\displaystyle P_o\) is the original price, and \(\displaystyle S\) is the percent to be discounted in decimal form.

A car ordinarily sells for \(\displaystyle \$ 21500\), but a savvy consumer walks out having paid only \(\displaystyle 70 \%\) of that price. How much did the customer pay?

Possible Answers:

\(\displaystyle \$ 15050\)

\(\displaystyle \$ 17500\)

\(\displaystyle \$6450\)

\(\displaystyle \$ 13030\)

\(\displaystyle \$ 16300\)

Correct answer:

\(\displaystyle \$ 15050\)

Explanation:

Applying our equation from above:

\(\displaystyle P_d = P_o(1-S)\) ---> \(\displaystyle P_d = \$ 21500 (.7) = \$15050\)

So, the customer paid \(\displaystyle \$ 15050\), or \(\displaystyle 70 \%\) of the original price.

Example Question #21 : Sale Prices

To find the sale price for a single item or group of like items, one can use the equation \(\displaystyle P_d = P_o(1-S)\), where \(\displaystyle P_d\) is the discounted price, \(\displaystyle P_o\) is the original price, and \(\displaystyle S\) is the percent to be discounted in decimal form.

Some clothes are on sale at \(\displaystyle 40 \%\) off retail. If a customer buys three pairs of jeans for a total of \(\displaystyle \$ 99\), what was the original price of one pair of jeans?

Possible Answers:

\(\displaystyle \$ 33\)

\(\displaystyle \$ 49\)

\(\displaystyle \$ 55\)

\(\displaystyle \$ 70\)

\(\displaystyle \$ 69\)

Correct answer:

\(\displaystyle \$ 55\)

Explanation:

We can apply our formula, but first we should divide the total price by \(\displaystyle 3\), then fill in what we know:

\(\displaystyle P_d = P_o(1-S)\) ---> \(\displaystyle \$ 33 = P_o(1-.4)\)

\(\displaystyle P_o = \frac{\$ 33}{.6} = \$ 55\)

So, one pair of jeans without discount costs \(\displaystyle \$ 55\).

Example Question #1297 : Act Math

To find the sale price for a single item or group of like items, one can use the equation \(\displaystyle P_d = P_o(1-S)\), where \(\displaystyle P_d\) is the discounted price, \(\displaystyle P_o\) is the original price, and \(\displaystyle S\) is the percent to be discounted in decimal form.

A pack of batteries is on sale for \(\displaystyle 85 \%\) of the normal price. If ten packs cost \(\displaystyle \$ 33.50\), what is the non-discounted price of one pack of batteries?

Round to the nearest \(\displaystyle \$ 0.01\).

Possible Answers:

\(\displaystyle \$ 3.94\)

\(\displaystyle \$ 3.54\)

\(\displaystyle \$ 3.14\)

\(\displaystyle \$ 3.74\)

\(\displaystyle \$ 3.34\)

Correct answer:

\(\displaystyle \$ 3.94\)

Explanation:

We can apply our formula, if we remember to first divide by \(\displaystyle 10\):

\(\displaystyle \frac{P_d}{10} = P_o(1-S)\) --->\(\displaystyle \frac{\$ 33.50}{10} = P_o(1-.15)\) 

\(\displaystyle \frac{\$ 3.35}{.85} = P_o = 3.9411 \approx \$ 3.94\)

Thus, our rounded answer is \(\displaystyle \$ 3.94\).

 

Example Question #31 : How To Find The Sale Price

To find the sale price for a single item or group of like items, one can use the equation \(\displaystyle P_d = P_o(1-S)\), where \(\displaystyle P_d\) is the discounted price, \(\displaystyle P_o\) is the original price, and \(\displaystyle S\) is the percent to be discounted in decimal form.

A video game is normally priced at \(\displaystyle \$ 65.00\). If the game is subsequently purchased for \(\displaystyle \$ 25.00\), what was the discount, as a percent, on the purchase?

Possible Answers:

\(\displaystyle 61.54 \%\)

\(\displaystyle 77.72 \%\)

\(\displaystyle 81.18 \%\)

There is not enough information to answer the question.

\(\displaystyle 57.22 \%\)

Correct answer:

\(\displaystyle 61.54 \%\)

Explanation:

To find the discount as a percent, simply divide the sale price by the original price, and multiply by \(\displaystyle 100\) (to convert from a decimal to a percent).

\(\displaystyle P_d = P_o(1-S)\) --> \(\displaystyle \frac{P_d}{P_o} =(1-S)\)

\(\displaystyle \frac{25}{65} =(1-S)\)

\(\displaystyle 100 (1-S) = 38.4615 \approx 38.46 \%\)

\(\displaystyle S \approx 61.54 \%\)

Thus, the game was purchased on a \(\displaystyle 61.54 \%\) discount.

Example Question #1293 : Act Math

To find the sale price for a single item or group of like items, one can use the equation \(\displaystyle P_d = P_o(1-S)\), where \(\displaystyle P_d\) is the discounted price, \(\displaystyle P_o\) is the original price, and \(\displaystyle S\) is the percent to be discounted in decimal form.

A steak dinner at Steaks 'R Us is normally priced at \(\displaystyle \$ 49.00\). The restaurant gives a discount to a preferred customer, and they eat for \(\displaystyle \$ 35.00\). What was the discount, as a percent, on the dinner?

Possible Answers:

\(\displaystyle 71.43 \%\)

\(\displaystyle 33.87 \%\)

\(\displaystyle 49.35 \%\)

\(\displaystyle 28.57 \%\)

\(\displaystyle 34.22 \%\)

Correct answer:

\(\displaystyle 28.57 \%\)

Explanation:

To find the discount as a percent, simply divide the sale price by the original price, and multiply by \(\displaystyle 100\) (to convert from a decimal to a percent).

\(\displaystyle P_d = P_o(1-S)\) --> \(\displaystyle \frac{P_d}{P_o} =(1-S)\)

\(\displaystyle \frac{35}{49} =(1-S) \approx 0.71428\)

\(\displaystyle 100 (1-S) = 71.428 \approx 71.43 \%\)

\(\displaystyle S \approx 28.57 \%\)

Thus, the game was purchased on approximately \(\displaystyle 28.57 \%\) discount.

Example Question #31 : How To Find The Sale Price

To find the sale price for a single item or group of like items, one can use the equation \(\displaystyle P_d = P_o(1-S)\), where \(\displaystyle P_d\) is the discounted price, \(\displaystyle P_o\) is the original price, and \(\displaystyle S\) is the percent to be discounted in decimal form.

Company A sells bicycles normally costing \(\displaystyle \$ 150\) for \(\displaystyle \$ 90\). Company B sells bicycles normally costing \(\displaystyle \$ 130\) for \(\displaystyle \$ 70\). Which company offers a greater discount, as a percentage?

Possible Answers:

There is not enough information to answer the question.

Company A

Company B

Both companies offer the same percentage discount.

Correct answer:

Company B

Explanation:

Here we are looking to solve our equation for \(\displaystyle S\). We need only to solve each equation for \(\displaystyle S\), with the bigger \(\displaystyle S\) representing the bigger percent discount.

\(\displaystyle P_d = P_o(1-S)\) ---> \(\displaystyle 1- \frac{P_d}{P_o} =S\)

For Company A: 

\(\displaystyle 1- \frac{90}{150} =S = \frac{60}{150} = \frac{2}{5} = 40 \%\)

For Company B:

\(\displaystyle 1- \frac{70}{130} = S = \frac{7}{13} \approx 53.85 \%\)

Thus, Company B offers the greater discount by percentage.

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