Question 1

Solve the problem.
-Midtown Antiques has found that sales have decreased 6\% from last year. Sales this year are \$ 132,724. Find the amount of last year's sales. Round your answer to the nearest dollar.

Accepted Answer

To find last year's sales, divide this year's sales by 0.94 (since sales decreased by 6%, they are now 94% of last year's sales): \$132,724 / 0.94 = \$141,196.

Question 2

Solve the problem.
-One half of a number is 3 more than one- sixth the same number. What is the number?

Accepted Answer

The answer of Solve the problem.
-One half of a number...

Question 3

Solve the problem.
-The sum of three consecutive integers is 363 . Find the integers.

Accepted Answer

The sum of three consecutive integers can be represented as $x + (x+1) + (x+2) = 3x + 3$. Setting this equal to 363 gives $3x + 3 = 363$. Solving for $x$, we get $3x = 360$, so $x = 120$. Therefore, the integers are 120, 121, and 122.

Question 4

Solve the problem.
-The sum of three consecutive odd integers is 213 . Find the integers.

Accepted Answer

The answer of Solve the problem.
-The sum of three consecutive...

Question 5

Solve the problem.
-If three times the smaller of two consecutive integers is added to four times the larger, the result is 46. Find the smaller integer.

Accepted Answer

Let the smaller integer be x. Then the larger integer is x+1. The equation is 3x + 4(x+1) = 46. Simplifying gives 3x + 4x + 4 = 46, which simplifies to 7x + 4 = 46. Solving for x gives x = 6.

Question 6

Solve the problem.
-Two angles of a triangle are $30^{\circ}$ and $100^{\circ}$. What is the measure of the third angle?

Accepted Answer

The sum of the angles in a triangle is $180^{\circ}$. Subtracting the given angles from $180^{\circ}$ gives the third angle: $180^{\circ} - 30^{\circ} - 100^{\circ} = 50^{\circ}$.

Question 7

Solve the problem.
-Find the measure of each angle in the triangle.

Accepted Answer

The answer of Solve the problem.
-Find the measure of each...

Question 8

Solve the problem.
-Find the measures of the supplementary angles.

Accepted Answer

The answer of Solve the problem.
-Find the measures of the...

Question 9

Solve the problem.
-Find the length of a rectangular lot with a perimeter of 126 meters if the length is 7 meters more than the width. $(\mathrm{P}=2 \mathrm{~L}+2 \mathrm{~W})$

Accepted Answer

The perimeter formula is $P = 2L + 2W$, where $P = 126$, $L = W + 7$. Substituting $L$ into the perimeter formula gives $126 = 2(W + 7) + 2W$, simplifying to $126 = 4W + 14$, and solving for $W$ gives $W = 28$. Thus, $L = W + 7 = 35$ meters.

Question 10

Solve the problem.
-A square plywood platform has a perimeter which is 10 times the length of a side, decreased by 24 . Find the length of a side.

Accepted Answer

The answer of Solve the problem.
-A square plywood platform has...

Question 11

Solve the problem.
-A rectangular Persian carpet has a perimeter of 232 inches. The length of the carpet is 20 inches more than the width. What are the dimensions of the carpet?

Accepted Answer

The perimeter of a rectangle is given by $2l + 2w$, where $l$ is the length and $w$ is the width. Given that the length is 20 inches more than the width ($l = w + 20$), and the perimeter is 232 inches, we can set up the equation $2(w + 20) + 2w = 232$. Simplifying, we get $4w + 40 = 232$, then $4w = 192$, and finally $w = 48$. Substituting back to find $l$, $l = 48 + 20 = 68$. Therefore, the dimensions are 48 inches by 68 inches.

Question 12

Solve the problem.
-A pie-shaped (triangular) lake-front lot has a perimeter of 2200 feet. One side is 200 feet longer than the shortest side, while the third side is 500 feet longer than the shortest side. Find the lengths of all three sides.

Accepted Answer

The shortest side is 500 ft, the second side is 700 ft (200 ft longer than the shortest), and the third side is 1000 ft (500 ft longer than the shortest). Their sum equals the perimeter of 2200 ft.

Question 13

Solve the problem.
-If Gloria received a 11 percent raise and is now making $\$ 22,200$ a year, what was her salary before the raise? Round to the nearest dollar if necessary.

Accepted Answer

To find the original salary before the raise, divide the new salary by 1.11 (since the raise was 11%). $\$ 22,200 \div 1.11 = \$ 20,000$.

Question 14

Solve the problem.
-On Monday, an investor bought 100 shares of stock. On Tuesday, the value of the shares went up $8 \%$. How much did the investor pay for the 100 shares if he sold them Wednesday morning for $\$ 1620$ ? Round to the nearest dollar if necessary.

Accepted Answer

The investor sold the shares for $1620 after they increased in value by 8%. To find the original price, divide $1620 by 1.08. This gives $1500, which is the amount the investor paid for the 100 shares.

Question 15

Solve the problem.
-At the end of the day, a storekeeper had $\$ 1155$ in the cash register, counting both the sale of goods and the sales tax of 5\%. Find the amount that is the tax. Round to the nearest dollar if necessary.

Accepted Answer

The total amount in the cash register is the sum of the sales and the sales tax. Let $x$ be the amount of sales before tax. The tax is 5% of $x$, or $0.05x$. The equation representing the total amount is $x + 0.05x = 1155$. Simplifying, $1.05x = 1155$. Solving for $x$, we get $x = 1100$. The tax is 5% of 1100, which is $0.05 \times 1100 = 55$. Therefore, the amount that is the tax is $\$55$.

Question 16

Solve the problem.
-Brand X copier advertises that its copiers run $18 \%$ longer between service calls than its competitor. If Brand X copiers run 66,600 copies between service calls, how many copies would the competitor run (to the nearest copy)?

Accepted Answer

The answer of Solve the problem.
-Brand X copier advertises that...

Question 17

Solve the problem.
-A high school graduating class is made up of 376 students. There are 96 more girls than boys. How many boys are in the class?

Accepted Answer

The total number of students is 376, and there are 96 more girls than boys. Let the number of boys be x. Then, the number of girls is x + 96. The equation to solve is x + (x + 96) = 376. Simplifying, 2x + 96 = 376, then 2x = 280, and finally x = 140. Therefore, there are 140 boys in the class.

Question 18

Solve the problem.
-Every basketball season Pam competes in a free throw contest. This year Pam was successful at 0.6 of her free throws. If she succeeded at 9 free throws, how many free throws did she attempt?

Accepted Answer

Pam's success rate is 0.6, and she succeeded at 9 free throws. To find the total attempts, divide the number of successful free throws by the success rate: 9 / 0.6 = 15.

Question 19

Solve the problem.
-CopyMart charges $\$ 28$ plus $44 \$$ per copy to produce promotional brochures. How many brochures can Steve purchase if he has a budget of $\$ 89.16$ ? (Hint: $44 \phi=\$ 0.44$ )

Accepted Answer

The total cost of producing $x$ brochures is $28+0.44x$. Since Steve has a budget of $89.16$, we have$$28+0.44x=89.16$$Solving for $x$, we get$$0.44x=61.16$$$$x=139$$Therefore, Steve can purchase 139 brochures.

Question 20

Solve the problem.
-Recently, the cost of 186 - oz jars of baby food was $\$ 11.52$. What was the cost of one jar?

Accepted Answer

To find the cost of one jar, divide the total cost by the number of jars: $11.52 / 6 = $1.92.

Quiz 2: Solving Equations and Inequalities

Solve the problem. -Midtown Antiques has found that sales have decreased 6\% from last year. Sales this year are \$ 132,724. Find the amount of last year's sales. Round your answer to the nearest dollar.

Solve the problem. -One half of a number is 3 more than one- sixth the same number. What is the number?

Solve the problem. -The sum of three consecutive integers is 363 . Find the integers.

Solve the problem. -The sum of three consecutive odd integers is 213 . Find the integers.

Solve the problem. -If three times the smaller of two consecutive integers is added to four times the larger, the result is 46. Find the smaller integer.

Solve the problem. -Two angles of a triangle are $30^{\circ}$ and $100^{\circ}$ . What is the measure of the third angle?

Solve the problem. -Find the measure of each angle in the triangle. $Solve the problem. -Find the measure of each angle in the triangle. A) 35^{\circ}, 103^{\circ}, 22^{\circ} B) 55^{\circ}, 13^{\circ}, 22^{\circ} C) 75^{\circ}, 75^{\circ}, 15^{\circ} D) 55^{\circ}, 103^{\circ}, 22^{\circ}$

Solve the problem. -Find the measures of the supplementary angles. $Solve the problem. -Find the measures of the supplementary angles. A) 96.25^{\circ} and 83.75^{\circ} B) 50.63^{\circ} and 39.38^{\circ} C) 202.5^{\circ} and 157.5^{\circ} D) 101.25^{\circ} and 78.75^{\circ}$

Solve the problem. -Find the length of a rectangular lot with a perimeter of 126 meters if the length is 7 meters more than the width. $(\mathrm{P}=2 \mathrm{~L}+2 \mathrm{~W})$

Solve the problem. -A square plywood platform has a perimeter which is 10 times the length of a side, decreased by 24 . Find the length of a side.

Solve the problem. -A rectangular Persian carpet has a perimeter of 232 inches. The length of the carpet is 20 inches more than the width. What are the dimensions of the carpet?

Solve the problem. -A pie-shaped (triangular) lake-front lot has a perimeter of 2200 feet. One side is 200 feet longer than the shortest side, while the third side is 500 feet longer than the shortest side. Find the lengths of all three sides.

Solve the problem. -If Gloria received a 11 percent raise and is now making $\$ 22,200$ a year, what was her salary before the raise? Round to the nearest dollar if necessary.

Solve the problem. -On Monday, an investor bought 100 shares of stock. On Tuesday, the value of the shares went up $8 \%$ . How much did the investor pay for the 100 shares if he sold them Wednesday morning for $\$ 1620$ ? Round to the nearest dollar if necessary.

Solve the problem. -At the end of the day, a storekeeper had $\$ 1155$ in the cash register, counting both the sale of goods and the sales tax of 5\%. Find the amount that is the tax. Round to the nearest dollar if necessary.

Solve the problem. -Brand X copier advertises that its copiers run $18 \%$ longer between service calls than its competitor. If Brand X copiers run 66,600 copies between service calls, how many copies would the competitor run (to the nearest copy) ?

Solve the problem. -A high school graduating class is made up of 376 students. There are 96 more girls than boys. How many boys are in the class?

Solve the problem. -Every basketball season Pam competes in a free throw contest. This year Pam was successful at 0.6 of her free throws. If she succeeded at 9 free throws, how many free throws did she attempt?

Solve the problem. -CopyMart charges $\$ 28$ plus $44 \$$ per copy to produce promotional brochures. How many brochures can Steve purchase if he has a budget of $\$ 89.16$ ? (Hint: $44 \phi=\$ 0.44$ )

Solve the problem. -Recently, the cost of 186 - oz jars of baby food was $\$ 11.52$ . What was the cost of one jar?

Quiz 2: Solving Equations and Inequalities

Solve the problem. -Midtown Antiques has found that sales have decreased 6\% from last year. Sales this year are \$ 132,724. Find the amount of last year's sales. Round your answer to the nearest dollar.

Solve the problem. -One half of a number is 3 more than one- sixth the same number. What is the number?

Solve the problem. -The sum of three consecutive integers is 363 . Find the integers.

Solve the problem. -The sum of three consecutive odd integers is 213 . Find the integers.

Solve the problem. -If three times the smaller of two consecutive integers is added to four times the larger, the result is 46. Find the smaller integer.

Solve the problem. -Two angles of a triangle are 30∘30^{\circ}30∘ and 100∘100^{\circ}100∘ . What is the measure of the third angle?

Solve the problem. -Find the measure of each angle in the triangle.

Solve the problem. -Find the measures of the supplementary angles.

Solve the problem. -Find the length of a rectangular lot with a perimeter of 126 meters if the length is 7 meters more than the width. (P=2 L+2 W) (\mathrm{P}=2 \mathrm{~L}+2 \mathrm{~W}) (P=2 L+2 W)