Exam 3: Equations, Inequalities and Problem Solving

At a university-sponsored concert, there were 3 times as many women as men. A total of 120 people attended the concert. How many men and how many women attended? Please enter your answer as two numbers, listed from least to greatest, separated by a comma.

Match these equations and their solutions. - $x = 6$

Solve the equation. 54 = $-$ 4 $-$ 13 a

Solve this equation. 6( x $-$ 6) $-$ 3( x $-$ 1) = 6

Suppose that Michael is paid two times his normal hourly rate for each hour he works over 43 hours in a week. Last week he earned $732 for 52 hours of work. What is his hourly wage?

Use the properties of equality to solve the equation. $\frac { 7 } { 16 } t = - \frac { 3 } { 28 }$

One of two supplementary angles is 35 times as large as the other. Find the measure of each angle.

An executive is earning $156,000 per year. This is $12,000 less than twice her salary 7 years ago. Find her salary 7 years ago. $ __________

Use the properties of equality to solve the equation. $\frac { 7 t } { 8 } = \frac { 7 } { 64 }$

For the following problem, solve the inequality. $15 \leq 10 t - 5 t - 20$

Solve the equation. 3 c + 5 = 20

For the following problem, solve the inequality. $2 x - 7 < 5$

Chris is following a 2,420-calorie-per-day diet plan. This plan permits 580 calories less than twice the number of calories permitted by Lerae's diet plan. How many calories are permitted by Lerae's plan?

Solve the equation. $3 ( 10 t + 1 ) = 6 ( 5 t - 1 )$

Solve the inequality. $3 t + 5 \geq 7 t - 7$

Use the properties of equality to solve the equation. $\frac { 5 } { 8 } m = 15$

Use the properties of equality to solve the equation. $- \frac { 7 } { 8 } t = 1$

If a satisfies an equation, then it is a root of the equation.

Solve the inequality. $3 x + 15 > 3 x + 13$

A nutrition plan counts grams of fat, carbohydrates, and fiber. The grams of carbohydrates are to be 17 more than twice the grams of fat. The grams of fiber are to be three less than the grams of fat. If the grams of carbohydrate, fat, and fiber must total 54 grams for a dinner meal, how many grams of each would be in the meal?