Question 1

Solve the problem.
-There is a relationship between the expected number of tickets sold for a raffle and the dollar value of the prize for the raffle. The equation T - 5P = 150 describes this relationship, where T is the expected number of tickets Sold, and P is the dollar value of the raffle prize. Suppose the expected ticket sales for a certain raffle are 2650. Substitute 2650 into the equation to determine the dollar value of the raffle prize.
A)$450
B)$2500
C)$500
D)$13,400

Accepted Answer

Substituting T = 2650 into the equation gives 2650 - 5P = 150. Solving for P, we get 2650 - 150 = 5P, which simplifies to 2500 = 5P. Dividing both sides by 5 gives P = 500.

Question 2

Use the five-step strategy for solving word problems to find the number or numbers described in the following exercise.
-One number exceeds another by -5. The sum of the numbers is -1. What are the numbers?
A)3 and 3
B)-4 and 3
C)-3 and 2
D)No solution

Accepted Answer

The correct numbers are -3 and 2. If we let one number be x and the other be x + (-5), their sum equals -1. Solving the system x + (x - 5) = -1 gives x = 2, so the other number is 2 - 5 = -3.

Question 3

Solve the problem.
-Suppose a cost-benefit model is given by $y = \frac { 2771 x } { 100 - x }$, where $y$ is the cost for removing $x$ percent of a given pollutant. What percent of pollutant can be removed for $\$ 36,000$ ? Round your answer to the nearest tenth of a percent.
A) $92.9 \%$
B) $108.3 \%$
C) $565.1 \%$
D) $9.3 \%$

Accepted Answer

To find the percent of pollutant that can be removed for $36,000, substitute $y = 36,000$ into the equation and solve for $x$:$$36,000 = \frac{2771x}{100 - x}$$Solving for $x$ gives approximately $92.9\%$.

Question 4

Use the five-step strategy for solving word problems to find the number or numbers described in the following exercise.
-When 10% of a number is added to the number, the result is 165. What is the number?
A)150
B)110
C)9
D)15

Accepted Answer

The equation for the problem is $x + 0.10x = 165$, which simplifies to $1.10x = 165$. Solving for $x$ gives $x = \frac{165}{1.10} = 150$.

Question 5

Use the five-step strategy for solving word problems to find the number or numbers described in the following exercise.
-When a number is decreased by 40% of itself, the result is 288. What is the number?
A)1200
B)8
C)192
D)480

Accepted Answer

The original number can be represented as x. When it is decreased by 40% of itself, it means we subtract 40% of x (which is 0.4x) from x, resulting in x - 0.4x = 0.6x. The equation then is 0.6x = 288. Solving for x gives x = 288 / 0.6 = 480.

Question 6

Determine whether the equation is an identity, a conditional equation, or an inconsistent equation.
-$$\frac { 3 x } { x - 6 } = \frac { 18 } { x - 6 } + 2$$
A) Identity
B) Conditional equation
C) Inconsistent equation

Accepted Answer

The answer of Determine whether the equation is an identity,...

Question 7

Solve the problem.
-A local race for charity has taken place since 1993. Using the actual speeds of the winners from 1993 through 1998, mathematicians obtained the formula y = 0.19x + 5, in which x represents the number of years after 1993 And y represents the winning speed in miles per hour. In what year is the winning speed predicted to be 7.28 Mph?
A)2006
B)2004
C)2007
D)2005

Accepted Answer

To find the year when the winning speed is predicted to be 7.28 mph, we substitute y = 7.28 in the given formula and solve for x:7.28 = 0.19x + 5Subtract 5 from both sides:2.28 = 0.19xDivide by 0.19:x = 2.28 / 0.19 = 12Since x represents the number of years after 1993, we add 12 to 1993 to find the year:1993 + 12 = 2005

Question 8

Solve the problem.
-A certain store has a fax machine available for use by its customers. The store charges $2.40 to send the first page and $0.45 for each subsequent page. The total price, P, for the faxing x pages can be modeled by the Formula P = 0.45(x - 1)+ 2.40. Determine the number of pages that can be faxed for $6.45.
A)14 pages
B)3 pages
C)57 pages
D)10 pages

Accepted Answer

To find the number of pages that can be faxed for $6.45, substitute $6.45 for P in the formula and solve for x: $6.45 = 0.45(x - 1) + 2.40. Simplifying, we get $6.45 = 0.45x - 0.45 + 2.40. Adding 0.45 to both sides gives $6.90 = 0.45x + 2.40. Subtracting 2.40 from both sides gives $4.05 = 0.45x. Dividing both sides by 0.45 gives x = 9. Since x represents the total number of pages, including the first page, the answer is 9 + 1 = 10 pages.

Question 9

Determine whether the equation is an identity, a conditional equation, or an inconsistent equation.
-$$\frac { - 7 x + 9 } { 7 } + \frac { 3 } { 7 } = - \frac { 2 x } { 7 }$$
A) Identity
B) Conditional equation
C) Inconsistent equation

Accepted Answer

This is a conditional equation because it can be simplified to a form where x can have a specific value. Simplifying the given equation, we get $-x + \frac{12}{7} = -\frac{2x}{7}$, which can be solved for a specific value of x, making it conditional on that value.

Question 10

Determine whether the equation is an identity, a conditional equation, or an inconsistent equation.
-$$\frac { 1 } { x + 7 } + \frac { 4 } { x + 5 } = \frac { - 2 } { x ^ { 2 } + 12 x + 35 }$$
A) Identity
B) Conditional equation
C) Inconsistent equation

Accepted Answer

The answer of Determine whether the equation is an identity,...

Question 11

Determine whether the equation is an identity, a conditional equation, or an inconsistent equation.
-$\frac { 11 x } { x } = 11$
A) Identity
B) Conditional equation
C) Inconsistent equation

Accepted Answer

The equation simplifies to $11 = 11$ for all $x$ except $x = 0$ (to avoid division by zero), making it an identity.

Question 12

Solve the problem.
-The U.S. Maritime Administration estimated that the cost per ton of building an oil tanker could be represented oy the model $y = \frac { 104,000 } { x + 235 }$, where $y$ is the cost in dollars per ton and $x$ is the tons (in thousands). What size of oil anker (in thousands of tons) can be built for $\$ 350$ per ton?
A) 178 thousand tons
B) 62 thousand tons
C) 532 thousand tons
D) 6 thousand tons

Accepted Answer

To find the size of the oil tanker, set $y = 350$ and solve for $x$:  $350 = \frac{104,000}{x + 235}$  Multiply both sides by $x + 235$:  $350(x + 235) = 104,000$  Expand:  $350x + 82,250 = 104,000$  Subtract 82,250 from both sides:  $350x = 21,750$  Divide by 350:  $x = 62$  So, the size of the oil tanker is 62 thousand tons.

Question 13

Solve the problem.
-The formula $\mathrm { y } = \frac { 25,000 + 270 \mathrm { x } } { \mathrm { x } }$ models the average cost per unit, $\mathrm { y }$, for Electrostuff to manufacture $\mathrm { x }$ units of Electrogadget IV. How many units must the company produce to have an average cost per unit of $\$ 380$ ?
A) 245 units
B) 227 units
C) 230 units
D) 93 units

Accepted Answer

To find the number of units ($x$) that result in an average cost per unit ($y$) of $380, substitute $380 for $y$ in the given formula and solve for $x$: $380 = \frac{25,000 + 270x}{x}$. Multiplying both sides by $x$ gives $380x = 25,000 + 270x$, which simplifies to $110x = 25,000$. Solving for $x$ gives $x = \frac{25,000}{110} = 227$.

Question 14

Determine whether the equation is an identity, a conditional equation, or an inconsistent equation.
-$$\frac { 5 } { y + 4 } - \frac { 2 } { y - 4 } = \frac { 5 } { y ^ { 2 } - 16 }$$
A) Identity
B) Conditional equation
C) Inconsistent equation

Accepted Answer

This is a conditional equation because it is true for specific values of $y$. The equation involves rational expressions, and its validity depends on the values of $y$ that do not make any denominator zero. The denominators suggest that $y \neq 4$ and $y \neq -4$, and the equation can be solved for specific values of $y$ that satisfy it, making it conditional.

Question 15

Solve the problem.
-A car rental agency charges $200 per week plus $0.25 per mile to rent a car. The total cost, C, for the renting the car for one week and driving it x miles can be modeled by the formula C = 0.25x + 200. How many miles can You travel in one week for $325?
A)281.25 miles
B)500 miles
C)475 miles
D)1300 miles

Accepted Answer

To find the number of miles you can travel for $325, substitute $325 for C in the formula and solve for x: $325 = 0.25x + 200. Subtract 200 from both sides to get $125 = 0.25x. Divide both sides by 0.25 to get x = 500 miles.

Question 16

Use the five-step strategy for solving word problems to find the number or numbers described in the following exercise.
-When four times the number is added to 7 times the number, the result is 44. What is the number?
A)-6.3
B)0.7
C)4
D)6.3

Accepted Answer

The equation to solve this problem is 4x + 7x = 44, which simplifies to 11x = 44. Solving for x gives x = 4.

Question 17

Solve the problem.
-The equation V = -3000t + 25,000 describes the value in dollars of a certain model of car after it is t years old. If a car is worth $13,000, substitute 13,000 into the equation to find the age of the car.
A)6 years
B)3 years
C)4 years
D)5 years

Accepted Answer

The equation V = -3000t + 25,000 describes the value in dollars of a certain model of car after it is t years old. If a car is worth $13,000, substitute 13,000 into the equation to find the age of the car.13,000 = -3000t + 25,000-12,000 = -3000tt = 4 years

Question 18

Find all values of x satisfying the given conditions.
-$y _ { 1 } = 7 x _ { 1 } y _ { 2 } = ( 6 x - 1 )$, and $y _ { 1 }$ exceeds $y _ { 2 }$ by 2 .
A) $\{ - 1 \rangle$
B) $\left\{ \frac { 1 } { 13 } \right\}$
C) $\{ 1 \}$
D) $\left\{ - \frac { 1 } { 13 } \right\}$

Accepted Answer

The answer of Find all values of x satisfying the...

Question 19

Use the five-step strategy for solving word problems to find the number or numbers described in the following exercise.
-When 4 times a number is subtracted from 7 times the number, the result is 24. What is the number?
A)0.7
B)8
C)-8
D)3

Accepted Answer

The equation to represent the problem is 7x - 4x = 24, simplifying to 3x = 24. Solving for x gives x = 8.

Question 20

Use the five-step strategy for solving word problems to find the number or numbers described in the following exercise.
-10% of what number is 92?
A)92
B)9.2
C)920
D)9200

Accepted Answer

To find the number of which 92 is 10%, you set up the equation 0.10 * x = 92, where x is the number you're trying to find. Solving for x gives x = 92 / 0.10 = 920.

Quiz 1: Equations and Inequalities

Use the five-step strategy for solving word problems to find the number or numbers described in the following exercise. -One number exceeds another by -5. The sum of the numbers is -1. What are the numbers?

Solve the problem. -Suppose a cost-benefit model is given by $y = \frac { 2771 x } { 100 - x }$ , where $y$ is the cost for removing $x$ percent of a given pollutant. What percent of pollutant can be removed for $\$ 36,000$ ? Round your answer to the nearest tenth of a percent.

Use the five-step strategy for solving word problems to find the number or numbers described in the following exercise. -When 10% of a number is added to the number, the result is 165. What is the number?

Use the five-step strategy for solving word problems to find the number or numbers described in the following exercise. -When a number is decreased by 40% of itself, the result is 288. What is the number?

Determine whether the equation is an identity, a conditional equation, or an inconsistent equation. - $\frac { 3 x } { x - 6 } = \frac { 18 } { x - 6 } + 2$

Determine whether the equation is an identity, a conditional equation, or an inconsistent equation. - $\frac { - 7 x + 9 } { 7 } + \frac { 3 } { 7 } = - \frac { 2 x } { 7 }$

Determine whether the equation is an identity, a conditional equation, or an inconsistent equation. - $\frac { 1 } { x + 7 } + \frac { 4 } { x + 5 } = \frac { - 2 } { x ^ { 2 } + 12 x + 35 }$

Determine whether the equation is an identity, a conditional equation, or an inconsistent equation. - $\frac { 11 x } { x } = 11$

Determine whether the equation is an identity, a conditional equation, or an inconsistent equation. - $\frac { 5 } { y + 4 } - \frac { 2 } { y - 4 } = \frac { 5 } { y ^ { 2 } - 16 }$

Solve the problem. -A car rental agency charges $200 per week plus $0.25 per mile to rent a car. The total cost, C, for the renting the car for one week and driving it x miles can be modeled by the formula C = 0.25x + 200. How many miles can You travel in one week for $325?

Use the five-step strategy for solving word problems to find the number or numbers described in the following exercise. -When four times the number is added to 7 times the number, the result is 44. What is the number?

Solve the problem. -The equation V = -3000t + 25,000 describes the value in dollars of a certain model of car after it is t years old. If a car is worth $13,000, substitute 13,000 into the equation to find the age of the car.

Find all values of x satisfying the given conditions. - $y _ { 1 } = 7 x _ { 1 } y _ { 2 } = ( 6 x - 1 )$ , and $y _ { 1 }$ exceeds $y _ { 2 }$ by 2 .

Use the five-step strategy for solving word problems to find the number or numbers described in the following exercise. -When 4 times a number is subtracted from 7 times the number, the result is 24. What is the number?

Use the five-step strategy for solving word problems to find the number or numbers described in the following exercise. -10% of what number is 92?