TExES Core Subjects 4-8: Calculations, Ratios & Proportions / Practice Exam

Angela uses a coupon for 15% off her order at the Burger Shack. If she orders a $3.50 burger, $2 fries and a $1.50 lemonade, how much will she save?

15% off means a discount of ($3.50 + $2 + $1.50) * 0.15 = $1.05.

A laptop's original price is $795. If it's on sale for 20% off, what is the sale price?

20% off means you are paying just 80% of the original price, so $795 * 0.8 = $636.

If it takes a team of three painters to paint a 7-room house in a day, how many painters are required to paint a 14-room house in a day?

3/7=x/14 x=6 3/7=6/14

Solve for x: 7/x = 28/16

A proportion is just two ratios that equal each other. In this case, x=4 because 7/4=28/16.

Which of the following is an example of a unit rate?

A unit rate is one where the denominator is 1.

A restaurant sells cheeseburgers to chicken sandwiches in a ratio of 7:2. If the restaurant sells 12 chicken sandwiches one day, how many cheeseburgers does it sell?

According to the ratio, for every 7 cheeseburgers sold, 2 chicken sandwiches are also sold. So, if 12 chicken sandwiches are sold one day, then the equivalent ratio will be 7 / 2 = x / 12. Solving for x, then gives an answer of x = 7 * 12 / 2 = 7 * 6 = 42.

The listed price of a dress is $59.99. If the tax is 8%, what is the total cost?

Convert 8% to a decimal. It becomes .08. Now, we can say that if x is the cost of the tax, then x = .08 * 59.99. That's 4.799, or 4.80 if we round it. Add $4.80 to $59.99 and we get $64.79.

Steve is trying to earn $300 in interest for a new guitar. He puts $2500 in an account that earns 2% interest yearly (simple interest). How long will it take to earn $300?

First, let's find out how much interest is earned in one year. $2500 X .02= $50/year $50 X 6 (years) = $300

As she enters college, Amy puts $500 in a savings account that earns 3.5% simple interest yearly. At the end of 4 years, how much money will be in the account?

I = Prt I = $500(0.035)(4 years) I = $70 The total in the account is principle + interest = $500 + $70 = $570

Arnold invested $7000 in his account and he had $8050 after 4 years. What was the yearly interest rate (simple interest)?

I = Prt Rearranging: I/(Pt) = r I = 1050 P = 7000 t = 4 1050/(7000∗4) = r 0.0375 = r Changing this to a percent: 0.0375 x 100 = 3.75%

How long will it take a car traveling at 32 mph to go 128 miles?

If t = d/r, then we have t = 128/32 = 4 hours

A pair of shoes is on sale for $96. If the shoes are on sale for 20% off, what was the original price?

If the shoes are 20% off that means you pay 80% of the original price. 80% is the same as 80/100. The proportion looks like this: 80/100 = 96/x x = 120

Angela invested $4000 in an account that earns 5% interest yearly (simple interest). She forgets about it for 12 years. What is the TOTAL amount of money in the account after those 12 years?

Interest = Prt I = $4000 X .05 x 12 = $2400 TOTAL $4000 principle + $2400 interest = $6400

A car goes 825 miles on 3 tanks of gas. How far can it go on 7 tanks of gas?

Let's just set up two ratios. First, 3 tanks goes 825 miles, so we have 3 tanks/825 miles. Next, there's 7 number of tanks to go x miles. Let's set these equal to each other and cross multiply. 3x = 825*7 825*7 = 5,775 5,775 /3 is 1925 miles

A bus travels 165 miles in 3 hours. What is its average speed?

Let's look at our distance formula: d = rt. Here we know our d is 165 and our t is 3. We want to know r. So we can rewrite the formula as r = d/t. r = 165 / 3 = 55 mph.

Olivia rides her bike at an average speed of 12 mph for 2 hours. How far does she go?

Let's start by identifying what we know from our formula. Our r, or rate, is 12 miles per hour. Our t, or time, is 2 hours. So d = 12 * 2. Our answer is 24 miles.

Philip is buying a video game that normally costs $85. It's on sale for 25% off. He has a coupon that will save him an extra 10% off the sale price. What is the cost he'll pay?

On sale for 25% off means he is paying 75% of $85, so $85 * 0.75 = $63.75. Now, an additional 10% off means paying 90% of $63.75, so $63.75 * 0.9 = $57.375 or $57.38.

An aquarium has 14 seals, 22 penguins and 4 sea turtles. What is the ratio of sea turtles to seals?

Remember that a ratio is a comparison. In the problem above we are comparing sea turtles to seals. We can write ratios with a colon that stands in for 'to.' So the correct answer is written 4:14, which stands for 4 sea turtles to 14 seals.

Mary buys a pair of jeans for $24.99, a skirt for $32.99 and a pair of shoes for $49.99. She has a coupon for 15% off the most expensive item. If the tax is 7.5%, what is the total cost?

The most expensive item here is the pair of shoes for $49.99. So 15% off $49.99 is 49.99 * 0.15 = 7.4985 or $7.50. So the pair of shoes end up costing $49.99 - $7.50 = $42.49. Now, with a 7.5% tax, her total is (24.99 + 32.99 + 42.49) * 1.075 = 108.00525 or $108.01.

Cassie buys a box of 36 batteries for 15 dollars. Express the rate in its simplest form.

The rate is written by writing as a fraction with the 36 in the numerator and the 15 in the denominator. You get 36 / 15 batteries / dollars. Simplifying, you get 12 / 5 batteries / dollars or 12 batteries / 5 dollars.

Kate is investing $1,000 and wants to double it in 8 years. What yearly, simple interest rate will she need to find?

To double her investment in 8 years, Kate needs to make $1,000 in interest in that time. We can set up our equation as I = Prt. I = 1000 P = 1000 t = 8 We are going to find r: 1000 = 1000 (r)(8) 0.125 = r The rate is 12.5 %.

A train travels at 60 mph for 5 hours, then slows to 50 mph for 2 hours. How many miles does it travel?

To find the distance plus distance, we need to tackle this problem in two parts. In the first part, the train travels at a rate of 60 mph for a time of 5 hours. With d = rt, we have d = 60 * 5. That's 300 miles. In the second part, the train travels at a rate of 50 mph for 2 hours. That's d = 50 * 2. So he went 100 miles in the second part. Now we add the two parts, 300 + 100, to get 400 miles.

If a car drives at 60 miles per hour for 4 hours, how far will it go?

Turning this into a mathematical expression, you get 60 miles / hour * 4 hours. Evaluating it, you get 240 miles.

Farmer John can till his field 1.5 times faster than Farmer Bob. If they work together, they can till the field in 6 hours. How long would it take Farmer John on his own?

Using the formula, you get 1/1.5J + 1/J = 1/6. Solving for J, you get this. 1/1.5J + 1.5/1.5J = 1/6 2.5/1.5J = 1/6 2.5*6 = 1.5J 15 = 1.5J J = 10

One hose can fill a swimming pool in 12 hours. A different, larger hose can fill the same pool in half the time. If both hoses are used together, how many hours will it take to fill the pool?

Using the formula, you get 1/12 + 1/6 = 1/t. Solving for t, you get this. 1/12 + 2/12 = 1/t 3/12 = 1/t 3t = 12 t = 4

Amy, Barry and Carter are building a fence. Together, it takes them 4 hours. If Amy worked alone, it would take her 14 hours. If Carter worked alone, it would take him 16 hours. Rounded to the nearest hour, how long would it take Barry to build the fence alone?

Using the formula, you get 1/14 + 1/16 + 1/B = 1/4. Solving for B, you get this. 8/112 + 7/112 + 1/B = 28/112 15/112 + 1/B = 28/112 1/B = 13/112 112 = 13B B = 8.6

Adam and Kevin are roommates. Adam can clean their apartment in 45 minutes. Kevin can clean it in 60 minutes. Rounded to the nearest minute, how much time will it take if they work together?

Using the formula, you get 1/45 + 1/60 = 1/t. Solving for t, you get this. 4/180 + 3/180 = 1/t 7/180 = 1/t 7t = 180 t = 25.7

Emily can rake her lawn in 5 hours. Andrew can rake the same lawn in 8 hours. Rounded to the nearest hour, how long will the job take if they work together?

Using the formula, you get 1/5 + 1/8 = 1/t. Now solving for t, you get this. 8/40 + 5/40 = 1/t 13/40 = 1/t 13t = 40 t = 3.08

A painting costs $225. If the sale price is $191.25, what is the percent discount?

x / 100 = 191.25 / 225 x = 85 So, 191.25 is 85% of the regular price. That means that the painting is discounted 15%. (100 - 85 = 15).