Exam 2: Equations, Inequalities, and Problem Solving

Solve. -How can $42,000 be invested, part at 4% annual simple interest and the remainder at 10% annual simple interest, so that the interest earned by the two accounts is equal at the end of the year?

Solve. -A 10-ft. board is cut into 2 pieces so that one piece is 2 feet longer than 3 times the shorter piece. If the shorter piece is x feet long, find the lengths of both pieces.

Solve. -The house numbers of two adjacent homes are two consecutive even numbers. If their sum is 358, find the house numbers.

Solve the formula for the specified variable. - $P = a + b + c$ for $b$

Solve. -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 $270,000, find each worker's salary.

Solve the equation for the indicated variable. - $I =$ Prt for $t$

Simplify the expression. First use the distributive property to remove any parentheses. --10(r + 2)

Solve. -The sum of three consecutive integers is 396. Find the numbers.

Solve the formula for the specified variable. - $A = \frac { 1 } { 2 } h ( B + b ) \quad$ for $B$

Solve. If needed, round money amounts to two decimal places and all other amounts to one decimal place. -The manager of a coffee shop has one type of coffee that sells for $7 per pound and another type that sells for $14 per pound. The manager wishes to mix 60 pounds of the $14 coffee to get a Mixture that will sell for $13 per pound. How many pounds of the $7 coffee should be used?

Graph the set of numbers given in interval notation. Then write an inequality statement in x describing the numbers graphed. - $( - \infty , 2 )$

Solve. If needed, round money amounts to two decimal places and all other amounts to one decimal place. -A chemist needs 170 milliliters of a 71% solution but has only 47% and 98% solutions available. Find how many milliliters of each that should be mixed to get the desired solution.

Write the following as an equation, using x for the unknown number. Then solve. -The sum of four times a number and 5 is equal to the difference of twice the number and $6 .$ Find the number.

Solve the inequality. Graph the solution set and write it in interval notation. - $4 x - 7 \geq 3 x - 6$

Simplify the expression by combining any like terms. - $7 a - 2 a + 5$

Solve the equation. - $\frac { 2 ( 7 - x ) } { 3 } = - x$

Solve the equation for the indicated variable. - $4 x - 7 y = 15 \quad$ for $y$

Solve the inequality. Graph the solution set and write it in interval notation. - $- 5 < 2 x - 3 < 0$

Solve. -Four times the difference of a number and one is equal to six times the sum of the number and three. Find the number.

Solve the inequality. Graph the solution set and write it in interval notation. - $x - 12 < - 1$