Exam 7: The Basic Concepts of Algebra

A chemist makes a mixture of concentrated hydrochloric acid and distilled water so that the ratio of acid to water is 4 to 3. If he starts with 20 liters of acid, how much water is mixed with the acid?

Provide an appropriate response. -2x - 5 = 5 + 7x - 3 Is this a linear equation?

Decide whether the statement translates into an expression or an equation. - $\frac { 2 } { 3 } \text { more than } 4 \text { times a number }$

Match the inequality with its correct representation. - $\{ x \mid x > 4 \}$

Tell which brand or which size is the better buy. -Brand A: $30 \mathrm { oz }$ for $\$ 9.00$ Brand B: $35 \mathrm { oz }$ for $\$ 10.85$

Solve the inequality, then graph the solution. - $- 5 < x + 1 < 4$

Solve the equation. - $4 + ( 3 - 3 x ) - ( 1 - x ) = 5 x - 2 ( x - 3 )$

Translate the verbal phrase into a mathematical expression. Use x to represent the unknown number. -Some number increased by 30

Solve the problem. -A car rental company has two rental rates. Rate 1 is $72 per day plus $.16 per mile. Rate 2 is $144 per day plus $.08 per mile. If you plan to rent for one week, how many miles would you need to Drive to pay less by taking Rate 2?

If $f$ varies jointly as $q ^ { 2 }$ and $h$ , and $f = 36$ when $q = 2$ and $h = 3$ , find $f$ when $q = 4$ and $h = 6$ .

Evaluate. - $- 90$

Solve the problem. -The number of births in County A has been increasing in recent years. Use the information given in the bar graph for the years 1960 and 1990, letting x = 0 represent the year 1960 and letting y represent the number of births. Use the graph to estimate the number of births in 1980.

Solve the problem. -Suppose the sales of a particular brand of appliance satisfy the relationship S(x)= 240x + 2000, where S(x)represents the number of sales in year x, with x = 0 corresponding to 1982. Find the Number of sales in 1988.

Determine the ratio and write it in lowest terms. -18 miles to 6 miles

If $\mathrm { f }$ varies jointly as $\mathrm { q } ^ { 2 }$ and $h$ , and $\mathrm { f } = 24$ when $\mathrm { q } = 2$ and $\mathrm { h } = 3$ , find $\mathrm { h }$ when $\mathrm { f } = 160$ and $\mathrm { q } = 4$ .

Solve the inequality, then graph the solution. - $- 10 < 3 b + 5 \leq 2$

The intensity I of light varies inversely as the square of the distance D from the source If the intensity of illumination on a screen 5 ft from a light is 2 foot-candles, find the intensity on a screen 15 ft from the light.

Solve the equation. - $\frac { 4 } { y } = \frac { 20 } { 10 }$

Solve the equation. - $\frac { 5 x } { 4 } - \frac { 3 x - 8 } { 5 } = \frac { 3 } { 4 }$

Stevie bought a stereo for $270 and put it on sale at his store at a 60% markup rate. What was the retail price of the stereo?