Question 1

Solve.
-One number is 8 less than three times a second number. The sum of the two numbers is 16. Find each number.

Accepted Answer

Let the second number be x. Then the first number is 3x - 8. The equation for their sum is x + (3x - 8) = 16, which simplifies to 4x - 8 = 16. Solving for x gives x = 6. Substituting x = 6 into the expressions for the two numbers gives the first number as 3(6) - 8 = 10 and the second number as 6. Therefore, the numbers are 6 and 10.

Question 2

Solve.
-The sum of one-half a number, one-third of the number, and one-twelfth of the number is 44. Find the original number.

Accepted Answer

The equation to represent the problem is (1/2)x + (1/3)x + (1/12)x = 44. Finding a common denominator, which is 12, and combining the fractions gives (6/12)x + (4/12)x + (1/12)x = 44, simplifying to (11/12)x = 44. Solving for x gives x = 44 * (12/11) = 48.

Question 3

Solve.
-Josh and Sam traveled in separate cars from their apartment to a ski resort 360 miles away. Sam wanted to get there early, so he traveled the maximum speed limit, 60 mph. Josh just bought a new car, so he drove a little
Slower at exactly 40 mph. If they both left at the same time, how much sooner did Sam arrive at the ski resort
Than Josh?

Accepted Answer

Sam took 6 hours (360 miles / 60 mph) and Josh took 9 hours (360 miles / 40 mph), so Sam arrived 3 hours sooner.

Question 4

Solve.
-A number is doubled and then decreased by 13. The result is 61. What is the original number?

Accepted Answer

The answer of Solve.
-A number is doubled and then decreased...

Question 5

Solve.
-Gary has a budget of $1930 to rent a computer for his company office. The computer company he wants to rent from charges $250 for installation and service as a one-time fee. Then they charge $105 per month rental for the
Computer. How many months will Gary be able to rent a computer with this budget?

Accepted Answer

First, subtract the one-time fee from the budget: $1930 - $250 = $1680. Then, divide the remaining budget by the monthly rental fee: $1680 / $105 = 16. Therefore, Gary can rent the computer for 16 months.

Question 6

Solve.
-Last year the yearly tuition at State University went up 20%. This year's charge for tuition for the year is $91,200. What was it last year before the increase went into effect?

Accepted Answer

Last year's tuition, before the 20% increase, can be found by dividing this year's tuition by 1.20 (since 20% increase means the cost is now 120% of the original, or 1.20 times the original). So, $91,200 / 1.20 = $76,000.

Question 7

Solve and graph the inequality.
-$$- 8 x - 11 > - 9 x - 3$$

Accepted Answer

The answer of Solve and graph the inequality.
-\[- 8 x...

Question 8

Solve and graph the inequality.
-$30 x + 15 - 5 ( 5 x + 1 ) \geq 0$

Accepted Answer

The answer of Solve and graph the inequality.
-\(30 x +...

Question 9

Solve.
-Charlotte invested $6000 in money market funds. Part was invested at 15% interest, the rest at 11% interest. At the end of each year the fund company pays interest. After one year she earned $764 in simple interest. How
Much was invested at each interest rate?

Accepted Answer

Charlotte invested $2600 at 15% and $3400 at 11%. Solving the system of equations: x + y = 6000 and 0.15x + 0.11y = 764, where x is the amount at 15% and y is the amount at 11%, gives x = 2600 and y = 3400.

Question 10

Solve for the variable
-$$\frac { 1 } { 4 } ( x + 8 ) + \frac { 1 } { 5 } ( x + 5 ) = x + 9$$

Accepted Answer

First, distribute the fractions across the parentheses: $\frac{1}{4}x + 2 + \frac{1}{5}x + 1 = x + 9$. Combine like terms: $\frac{9}{20}x + 3 = x + 9$. Subtract $\frac{9}{20}x$ and 9 from both sides: $-6 = \frac{11}{20}x$. Solve for $x$: $x = -\frac{120}{11}$.

Question 11

Solve and graph the inequality.
-$$- 6 ( 4 x + 5 ) < - 30 x - 42$$

Accepted Answer

The answer of Solve and graph the inequality.
-\[- 6 (...

Question 12

Solve and graph the inequality.
-$$\frac { 1 } { 7 } ( x + 4 ) \leq \frac { 2 } { 7 } ( x + 8 )$$

Accepted Answer

The answer of Solve and graph the inequality.
-\[\frac { 1...

Question 13

Solve.
-In a triangle, the measure of the first angle is four times the measure of the second angle. The measure of the third angle is 144 degrees more than the second angle. What is the measure of the first angle?

Accepted Answer

The first angle is four times the second angle, so the first angle is 4x and the second angle is x. The third angle is 144 degrees more than the second angle, so the third angle is x + 144. The sum of the angles in a triangle is 180 degrees, so 4x + x + x + 144 = 180. 6x + 144 = 180. 6x = 36. x = 6. The first angle is 4x, so the first angle is 4(6) = 24 degrees.

Question 14

Solve.
-Nancy has $5.30 in change. She has three times as many nickels as quarters. She has two more quarters than dimes. How many coins of each type does he have?

Accepted Answer

Nancy has $5.30 in change. Let the number of quarters be q, dimes be d, and nickels be n. We have three equations based on the information:1. $0.25q + 0.10d + 0.05n = 5.30$2. $n = 3q$3. $q = d + 2$Substituting the values from equations 2 and 3 into equation 1 and solving gives us q = 11, d = 9, and n = 33. Therefore, Nancy has 11 quarters, 9 dimes, and 33 nickels.

Quiz 2: Equations, Inequalities, and Applications

Solve. -One number is 8 less than three times a second number. The sum of the two numbers is 16. Find each number.

Solve. -The sum of one-half a number, one-third of the number, and one-twelfth of the number is 44. Find the original number.

Solve. -A number is doubled and then decreased by 13. The result is 61. What is the original number?

Solve. -Last year the yearly tuition at State University went up 20%. This year's charge for tuition for the year is $91,200. What was it last year before the increase went into effect?

Solve and graph the inequality. - $- 8 x - 11 > - 9 x - 3$ $Solve and graph the inequality. - - 8 x - 11 > - 9 x - 3 A) x \leq - 14 B) x > 8 C) x \geq - 14 D) x < 8$

Solve and graph the inequality. - $30 x + 15 - 5 ( 5 x + 1 ) \geq 0$ $Solve and graph the inequality. - 30 x + 15 - 5 ( 5 x + 1 ) \geq 0 A) x \leq - 2 B) x \geq - 2 C) x > - 2 D) x < - 2$

Solve. -Charlotte invested $6000 in money market funds. Part was invested at 15% interest, the rest at 11% interest. At the end of each year the fund company pays interest. After one year she earned $764 in simple interest. How Much was invested at each interest rate?

Solve for the variable - $\frac { 1 } { 4 } ( x + 8 ) + \frac { 1 } { 5 } ( x + 5 ) = x + 9$

Solve and graph the inequality. - $- 6 ( 4 x + 5 ) < - 30 x - 42$ $Solve and graph the inequality. - - 6 ( 4 x + 5 ) < - 30 x - 42 A) x < - 2 B) x \geq - 2 C) x \leq - 2 D) x > - 2$

Solve and graph the inequality. - $\frac { 1 } { 7 } ( x + 4 ) \leq \frac { 2 } { 7 } ( x + 8 )$ $Solve and graph the inequality. - \frac { 1 } { 7 } ( x + 4 ) \leq \frac { 2 } { 7 } ( x + 8 ) A) x \leq - 12 B) x \geq 12 C) x \leq 12 1ecb336_8657_804c_a9b7_c38f1700487d_TB6914_00 D) x \geq - 12$

Solve. -In a triangle, the measure of the first angle is four times the measure of the second angle. The measure of the third angle is 144 degrees more than the second angle. What is the measure of the first angle?

Solve. -Nancy has $5.30 in change. She has three times as many nickels as quarters. She has two more quarters than dimes. How many coins of each type does he have?