Question 1

Solve the problem.
-If 5 is increased to 8, the increase is what percent of the original number?

Accepted Answer

The increase is 3 (from 5 to 8), which is 3/5 of the original number. Converting this fraction to a percentage gives 3/5 = 0.6, and 0.6 * 100% = 60%.

Question 2

Let x represent the number. Write the English phrase as an algebraic expression.
-Five times a number, decreased by 19.

Accepted Answer

The phrase "Five times a number, decreased by 19" translates to multiplying the number (x) by 5 and then subtracting 19, which is represented by the expression 5x - 19.

Question 3

Let x represent the number. Write the English phrase as an algebraic expression.
-The product of 6 and a number, added to 14.

Accepted Answer

The phrase "The product of 6 and a number, added to 14" translates to 6 times a number (6x) plus 14, which is represented by the expression 14 + 6x.

Question 4

Let x represent the number. Write the English phrase as an algebraic expression.
-Eleven times a number decreased by one-third of the same number.

Accepted Answer

The correct expression is $11x - \frac{x}{3}$ because it represents multiplying the number $x$ by 11 and then subtracting one-third of the same number $x$.

Question 5

Solve the problem.
-If 100 is decreased to 95, the decrease is what percent of the original number?

Accepted Answer

The decrease is 5 (100 - 95), which is 5% of the original number 100 (5/100 = 0.05 or 5%).

Question 6

The pie chart below shows the number of pizzas consumed by college students in a typical month. Use the chart to
answer the question. 
-What percent of college students consume 3 or more pizzas in a typical month?

Accepted Answer

57% of college students consume 3 or more pizzas in a typical month. This statistic reflects the popularity of pizza among college students, likely due to its convenience, affordability, and taste.

Question 7

Let x represent the number. Use the given conditions to write an equation. Solve the equation and find the number.
-The sum of four times a number and 6 is equal to the difference of twice the number and 10. Find the number.

Accepted Answer

The correct equation that represents the given conditions is $4x + 6 = 2x - 10$. Solving this equation for $x$ gives $x = -8$.

Question 8

Let x represent the number. Write the English phrase as an algebraic expression.
-Twice the sum of a number and -16.

Accepted Answer

The correct expression is 2(x + (-16)), which translates to "twice the sum of a number and -16."

Question 9

Let x represent the number. Use the given conditions to write an equation. Solve the equation and find the number.
-If 5 times a number is added to -7, the result is equal to 12 times the number. Find the number.

Accepted Answer

The correct equation that represents the given condition is 5x + (-7) = 12x. Solving this equation for x gives the number as -1.

Question 10

Let x represent the number. Write the English phrase as an algebraic expression.
-The product of -29 and the sum of a number and 17.

Accepted Answer

The phrase "the product of -29 and the sum of a number and 17" translates to multiplying -29 by the expression (x + 17), which is represented as -29(x + 17).

Question 11

Let x represent the number. Use the given conditions to write an equation. Solve the equation and find the number.
-Four times a number added to 7 times the number equals 55. Find the number.

Accepted Answer

The correct equation that represents the given condition is $4x + 7x = 55$. Solving this equation, $11x = 55$, gives $x = 5$.

Question 12

Let x represent the number. Use the given conditions to write an equation. Solve the equation and find the number.
-30 marbles are to be divided into three bags so that the second bag has three times as many marbles as the first bag and the third bag has twice as many as the first bag. If x is the number of marbles in the first bag, find the
Number of marbles in each bag.

Accepted Answer

The answer of Let x represent the number. Use the...

Question 13

The pie chart below shows the number of pizzas consumed by college students in a typical month. Use the chart to
answer the question. 
-What percent of college students consume 4 pizzas or less in a typical month?

Accepted Answer

The answer of The pie chart below shows the number...

Question 14

Let x represent the number. Write the English phrase as an algebraic expression.
-The quotient of 37 times a number and -3.

Accepted Answer

The phrase "the quotient of 37 times a number and -3" translates to dividing the product of 37 and a number (represented as $37x$) by -3, which is mathematically expressed as $\frac { 37 x } { - 3 }$.

Question 15

The pie chart below shows the number of pizzas consumed by college students in a typical month. Use the chart to
answer the question. 
-If State University has approximately 25,000 students, about how many would you expect to consume 5-6 pizzas in a typical month?

Accepted Answer

Based on the Pareto principle, which suggests that roughly 80% of effects come from 20% of causes, if we apply this to pizza consumption among students, we might expect that 20% of the students consume 80% of the pizza. Therefore, 20% of 25,000 students is 5,000. However, since the question specifies a range of 5-6 pizzas, which might not represent the highest consumption but rather a significant portion, a slightly lower figure like 4,500 students (A) is a reasonable estimate without more specific data.

Question 16

Solve the problem.
-Due to a lack of funding, the number of students enrolled at City College went from 8000 last year to 3000 this year. Find the percent decrease in enrollment. (Round to the nearest tenth of a percent, if necessary.)

Accepted Answer

The percent decrease in enrollment is calculated by the formula: [(Original Number - New Number) / Original Number] * 100. So, [(8000 - 3000) / 8000] * 100 = 62.5%.

Question 17

Let x represent the number. Use the given conditions to write an equation. Solve the equation and find the number.
-Three-fourths of a number is 56 . Find the number in lowest terms.

Accepted Answer

Three-fourths of a number is 56. So, $\frac { 3 } { 4 } x = 56$. Solving for x, we get x = $\frac { 4 } { 3 } \times 56 = \frac { 224 } { 3 } = \frac { 112 } { 3 } = \frac { 10 } { 9 }$.

Question 18

Let x represent the number. Write the English phrase as an algebraic expression.
-The quotient of 31 and the product of a number and $- 10$.

Accepted Answer

The phrase "the quotient of 31 and the product of a number and -10" translates to dividing 31 by the product of the number (x) and -10, which is represented as $\frac { 31 } { - 10 x }$.

Question 19

Let x represent the number. Use the given conditions to write an equation. Solve the equation and find the number.
-When 5 times a number is subtracted from 7 times the number, the result is 22. Find the number.

Accepted Answer

The correct equation that represents the given condition is 7x - 5x = 22. Solving this equation, 2x = 22, gives x = 11.

Question 20

Let x represent the number. Use the given conditions to write an equation. Solve the equation and find the number.
-The president of a certain university makes three times as much money as one of the department heads. If the total of their salaries is $180,000, find each worker's salary.

Accepted Answer

Let the department head's salary be x. Then, the president's salary is 3x. The equation is x + 3x = 180,000. Solving for x gives x = 45,000, so the president's salary is 3x = 135,000.

Quiz 2: Linear Equations and Inequalities in One Variable

Solve the problem. -If 5 is increased to 8, the increase is what percent of the original number?

Let x represent the number. Write the English phrase as an algebraic expression. -Five times a number, decreased by 19.

Let x represent the number. Write the English phrase as an algebraic expression. -The product of 6 and a number, added to 14.

Let x represent the number. Write the English phrase as an algebraic expression. -Eleven times a number decreased by one-third of the same number.

Solve the problem. -If 100 is decreased to 95, the decrease is what percent of the original number?

The pie chart below shows the number of pizzas consumed by college students in a typical month. Use the chart to answer the question. -What percent of college students consume 3 or more pizzas in a typical month?

Let x represent the number. Use the given conditions to write an equation. Solve the equation and find the number. -The sum of four times a number and 6 is equal to the difference of twice the number and 10. Find the number.

Let x represent the number. Write the English phrase as an algebraic expression. -Twice the sum of a number and -16.

Let x represent the number. Use the given conditions to write an equation. Solve the equation and find the number. -If 5 times a number is added to -7, the result is equal to 12 times the number. Find the number.

Let x represent the number. Write the English phrase as an algebraic expression. -The product of -29 and the sum of a number and 17.

Let x represent the number. Use the given conditions to write an equation. Solve the equation and find the number. -Four times a number added to 7 times the number equals 55. Find the number.

The pie chart below shows the number of pizzas consumed by college students in a typical month. Use the chart to answer the question. -What percent of college students consume 4 pizzas or less in a typical month?

Let x represent the number. Write the English phrase as an algebraic expression. -The quotient of 37 times a number and -3.

The pie chart below shows the number of pizzas consumed by college students in a typical month. Use the chart to answer the question. -If State University has approximately 25,000 students, about how many would you expect to consume 5-6 pizzas in a typical month?

Solve the problem. -Due to a lack of funding, the number of students enrolled at City College went from 8000 last year to 3000 this year. Find the percent decrease in enrollment. (Round to the nearest tenth of a percent, if necessary.)

Let x represent the number. Use the given conditions to write an equation. Solve the equation and find the number. -Three-fourths of a number is 56 . Find the number in lowest terms.

Let x represent the number. Write the English phrase as an algebraic expression. -The quotient of 31 and the product of a number and $- 10$ .

Let x represent the number. Use the given conditions to write an equation. Solve the equation and find the number. -When 5 times a number is subtracted from 7 times the number, the result is 22. Find the number.

Let x represent the number. Use the given conditions to write an equation. Solve the equation and find the number. -The president of a certain university makes three times as much money as one of the department heads. If the total of their salaries is $180,000, find each worker's salary.