Exam 7: The Basic Concepts of Algebra

Solve the problem. -The Consumer Price Index provides a means of determining the purchasing power of the U.S. dollar from one year to the next. To use the Consumer Price Index to predict a price in a particular Year, we can set up a proportion and compare it with a known price in another year as follows: $\frac { \text { price in year } \mathrm { A } } { \text { index in year } \mathrm { A } } = \frac { \text { price in year } \mathrm { B } } { \text { index in year } \mathrm { B } } \text {. }$ In 1994 the Consumer Price Index was 148.2 and in 2000 it was 172.2. Find the amount that would Be charged in 2000 for the use of the same amount of electricity that cost $180 in 1994. Give your Answer to the nearest dollar.

Solve the equation. - $6 n - 7 = 41$

Solve the inequality, giving its solution set in both interval and graph forms. - $3 x < - 27$

Bert is 19.5 kilometers away from Brenda. Both begin to walk toward each other at the same time. Bert walks at 4 kilometers per hour. They meet in 3 hours. How fast is Brenda walking?

Solve the inequality, then graph the solution. - $2<1-4 x \leq 6$

In a recent school board election, the two candidates for president together received 2111 votes. The loser received 803 fewer votes than the winner. How many votes did the winner receive?

Solve the inequality, giving its solution set in both interval and graph forms. - $0.25 \mathrm { k } > 6$

Match the inequality with its correct representation. -

Evaluate the expression. - $\left( \frac { 4 } { 9 } \right) ^ { 3 }$

Decide whether the equation is "conditional," an "identity," or a "contradiction." Give its solution set. - $15 m + 15 = 3 ( 3 m - 5 )$

Solve the equation. - $\frac { p } { 3 } - \frac { 3 p } { 8 } = 2$

Behemoth Back Packs, Inc. finds that the cost to make x back packs is C = 90x + 6396, while the revenue produced from them is R = 137x (C and R are in dollars). What is the smallest whole Number of back packs, x, that must be sold for the company to show a profit?

Solve the equation. - $\frac { ( r + 6 ) } { 3 } = \frac { ( r + 8 ) } { 6 }$

Evaluate the expression. - $- 5 ^ { - 4 }$

Jay drove 340 kilometers at the average rate of 68 kilometers per hour. How long did the trip take?

Solve the equation. - $- 6 a + 5 + 7 a = 9 - 27$

Solve the problem. -Suppose y = mx + b is a mathematical model for actual time as a function of estimated time, where y represents actual time and x represents estimated time and m and b are constants. If m = 2 and B = -1.2, find y when x is 30 min.

Decide whether the equation is "conditional," an "identity," or a "contradiction." Give its solution set. - $5 ( 5 g - 28 ) - 25 g + 140 = 0$

Determine the ratio and write it in lowest terms. -86 inches to 6 feet

Solve the equation. - $- 0.05 ( 500 ) + 0.08 \mathrm { x } = 0.03 ( 500 + \mathrm { x } )$