# TEAS Math Practice Test 3

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#### | 2x − 5 | = 19 Which of the following is the solution set for the equation above?

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Absolute value equations can be rewritten in two ways to solve: 2x − 5 = 19 and 2x − 5 = −19. Solve both: 2x − 5 = 19 2x = 24 X = 12 2x − 5 = −19 2x = −14 x = −7 The two solutions and −7 and 12.

#### If Maria left a \$10.16 tip on a breakfast that cost \$86.89, approximately what percentage was the tip?

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The easiest way to answer this question is to round the numbers. Let’s say the tip is \$10 and the total was \$87. \$10/\$87 = approximately 11%. (A) is the closest answer to our approximation.

#### A nurse working at a medical clinic earns \$17.81 per hour. The nurse works three 8-hour shifts and one 12-hour shift every week, and is paid weekly. Weekly deductions are: federal tax \$102.80, state tax \$24.58, federal insurance \$18.13, and family health insurance \$52.15. What is the nurse's take-home pay each week?

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First you must calculate how many hours the nurse works each week. Three 8-hour shifts plus one 12-hour shift equals 36 hours per week. Beginning Salary = 36 x \$17.81 = \$641.16 Deductions = \$102.80 + \$24.58 + \$18.13 + \$52.15 = \$197.66 Take-Home Pay = \$641.16 − \$197.66 = \$443.50

#### How many imperial gallons are there in 1,400 liters?

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There are 1,000 liters in 1 kiloliter: 1,400 liters = 1.4 kiloliters. 1.4 x 220 = 308 imperial gallons

#### Derek purchased concert tickets in the month of June for \$73, \$66, \$96, \$17, and \$66 dollars. Which of the following is an accurate estimate of the total amount he spent on concert tickets in June?

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The easiest way to make an estimate is to round each number so there is only one nonzero digit. Then you can easily add up the numbers: 73 ≈ 70 66 ≈ 70 96 ≈ 100 17 ≈ 20 66 ≈ 70 Adding these numbers together yields \$330.

#### 5y − 8 > 32

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To solve an inequality, simply treat the inequality symbol as if it’s an equals sign: 5y − 8 > 32 5y > 40 y > 8

#### There are 48 students studying foreign language at the community college. If the only two foreign languages offered are French and Spanish, and 28 students are studying French, which of the following represents the ratio of students studying Spanish to the total number of foreign language students?

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If there are 48 total, and 28 study French, then 20 study Spanish. The ratio of 20 to 48 = 10/24 = 5/12.

#### What is 181.5% of 18?

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First you must convert the fraction to a decimal by moving the decimal point 2 places to the left, which gives you 1.815. Then multiply this by 18. 1.815 x 18 = 32.67

#### Which of the following is equivalent to 0.0009?

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In order to convert a decimal to a percent you need to move the decimal point two places to the right and add the percent symbol.

#### The hourly rate for a male went up to \$13.50 from \$12.50. How much of a raise did he receive?

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Subtract the second number from the original/first number (13.5-12.5=1.0) and divide the result by the original number (1/12.5=0.08=8%) to determine the percent of growth.

#### What is the cost of a DVD without the sales tax if you buy \$22.90 for one that has a 7% sales tax included?

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assuming that y is the DVD's cost before tax. When tax was added, the price would be y + 0.07y = \$22.90. Because of this, 1.07y=22.90, or y=22.90/1.07=21.40. Be careful not to simply deduct 7% from \$22.90. This is untrue.

#### A toll costs \$2 for a vehicle and the driver, and an additional 75 cents for each passenger. How many people are in the automobile in total if the toll is \$4.25?

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\$2 of the \$4.25 toll goes toward the driver and vehicle. This leaves \$2.25 (\$4.25-\$2) for the passengers. There are 1 driver and 3 passengers overall, thus \$2.25/0.75 equals 3 passengers.

#### Leaving San Diego at 6:15 p.m. PST, a jet touched down in Philly at 2:45 a.m. EST. How much time was the flight?

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To begin with, change 6:15 PST to 9:15 EST. The flight then took place between 9:15 p.m. and 2:45 a.m. EST. Thus, the flight's duration was 5 1/2 hours.

#### Cost per square yard for carpet is \$3. The carpeting-ready space measures 12 feet by 18 feet. What is the price of the carpet?

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12 feet by 18 feet is equal to 24 square yards (4 yards by 6 yards). \$24 divided by \$3 per square yard equals \$72. Although 9 square feet equal one square yard, keep in mind that 3 feet equals one yard.

#### A product's initial price is \$125. What is the price of the goods if it is first discounted by 20% and then further discounted by 30%?

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Instead of simply adding discounts, you must apply them sequentially. Thus, the price after the initial 20% discount is \$125 x 80% = \$100. The price after the second 30% discount is \$100 x 70%, or \$70.

#### Three baseball cards, three football cards, and six hockey cards make up a stack of sports cards. What is the likelihood that a hockey card will be chosen at random from a deck of cards?

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There are a total of 12 cards. As a result, the likelihood of selecting a hockey card is 6/12, or half.

#### When x + y = z and x + y + 15 = 30, 40 - z =

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If x + y + 15 = 30, then z + 15 = 30 (use x + y to replace x) indicating that z = 15. z = 15, then 40 - z = 40 - 15 = 25 if z = 15.

#### Of the following, which one is NOT a prime number?

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Given that it equals 31 x 3, the number 93 is not a prime. A integer is divisible by three if all of its digits, when added together, are divisible by three.

#### (x+3)(x+5) =

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Use the First, Outside, Inside, Last (FOIL) approach to solve. X² +3x +5x + 3×5

#### What does 4(x-y)+7 equal if x = y?

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In the second equation, you can substitute x for y if x = y, hence 4(x-x)+7 = 4(0)+7=7

#### How does 96 / 92 equal

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Keep the base and subtract the exponents when dividing two powers with the same base.

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