Algebra and Geometry basics

One customer received a 25% discount on a $300 bill. The second customer received an 8% discount on a $300 bill. The third customer received a 5% discount on a $300 bill. What was the total amount discounted to the three customers?

$114.00

A plumber sells 100 sets of bathroom fixtures at $165.00 per set. At 16% what would his commission be?

$2,640.00

If your pay is $52.00 a month, how much will you earn in a year?

$624.00 per year

A loss of $13.50 on a washing machine represents 15% loss on the selling price. What is the selling price?

$90.00

Do the values a=4, b=6, and c=9, make a right triangle? (use pythagorean theorem)

*NO* a² ⁺ b² = c² 4² ⁺ 6² = 9² 16 ⁺ 36 = 81 52 = 81 *52 does not equal 81, therefore the values do not make a right triangle*

Do the values a=5, b=12, and c=13, make a right triangle? (use pythagorean theorem formula)

*YES* a² ⁺ b² = c² 5² ⁺ 12² = 13² 25 ⁺ 144 = 169 169 = 169 *169 equals 169, therefore the values make a right triangle*

Multiply .014 by .0064

.0000896

Multiply .214 by .303

.064842

Find the decimal equivalent to the nearest thousandths: 7/64

.109

Find the decimal equivalent to the nearest thousandths: 3/4

.750

Find the decimal equivalent to the nearest thousandths: 28/32

.875

Find the decimal equivalent to the nearest thousandths: 56/64

.875

Find 1/2 of 1% of 190 tons.

.95 tons

Find the decimal equivalent to the nearest thousandths: 31/32

.969

How many tiles 9 inches square will be necessary to floor a room measuring 35 feet by 20 feet? (Round off to nearest tile)

1,244 tiles

5% of 160

100% = 160 10% = 16 1% = 1.6 1.6 x 5 = 8 *8*

3% of 280

100% = 280 10% = 28 1% = 2.8 2.8 x 3 = 8.4 *8.4*

A meal costs $56.24. The tax is 9%. what's the total cost of the meal?

100% = 56.24 10% = 5.624 1% = 0.5624 5.624 - 0.5624 = 5.56776 (or 5.57 rounded up) total cost: 56.24 + 5.57 = $61.81 *$61.81*

A company marched 48 miles in 5 days. The first day they marched 12 miles, the second day 9 miles, the third day 7 miles, the fourth day 9 miles. How many miles did they march the last day?

11 miles

Find 12.5 % of 96 men.

12 men

It takes 5 lbs. of cement to cover 10 square feet. How many lbs. of cement will be needed to cover a rectangular area 25 ft. by 10 ft.?

125 lbs = x

A dealer bought 3 loads of coal weighing 6,242 lbs., 28,394 lbs. and 143,686 lbs. How much did he buy in all?

178,322 lbs. total

620.75 divided by .25 equals

2483

A truck carrying 6,750 lbs. of lead weighed 9,000 lbs. What percent of the total weight was due to the weight of the truck?

25%

If an automobile travels 450 yards in 15 seconds, how many feet does it go in 1/3 of a second?

30 feet

Add the following numbers: 4,585,285 plus 792 plus 73,214.

4,659,291

Find the area of a circle that has a radius of 12 inches.

452.3904 sq. in.

120 is what percent of 240?

50%

Two machinists operating the same lathe, work 10 hours each on a day shift and on a night shift, respectively. One man turns out 400 pieces an hour, the other 600 pieces an hour. What will be the difference in their output at the end of 30 days?

60,000 pieces

If it takes 5 hours to do 2/3 of a job, how long will it take to complete the job?

7.5 hours = 1 job

Your grades on 5 tests were 80%, 90%, 70%, 60% and 50%. What is the average of your 5 grades?

70%

Find the volume of a rectangular solid 20 ft. wide, 28 ft. long and 16 ft. high.

8,960 cubic ft.

225 is 25% of what amount?

900 = ?

area of a parallelogram formula

A = b × h b = base h = height area of a parallelogram is the base length multiplied by the height

Penny needs to buy carpet for her rectangular bedroom. The height is 13 feet and the base is 7 feet. At $4 a foot, how much will Penny's carpet cost? (use area of a rectangle formula)

A = l × w A = 13 × 7 A = 91 the area of his bedroom is 91 feet 91 × $4 = $364 Penny's carpet will cost $364

area of a rectangle formula

A = l × w l = length w = width area of a rectangle is length multiplied by the width

Jim needs to find out how much grass to buy to fill the surface of his triangular yard. If the base of his yard is 12 feet and the height of his yard is 15 feet. At $3 a foot, how much will he have to pay for all his grass? (use area of a triangle formula)

A = ½ × b × h A = ½ × 12 × 15 A = 90 the area of his yard is 90 feet 90 × $3 = $270 Jim will have to pay $270

area of a triangle formula

A = ½ × b × h b = base h = height area of a triangle is one half multiplied by the base length multiplied by the height if the base and the height are known, we can use the formula

Anna needs to buy flooring for her circular elevator room. The diameter is 6 feet and the radius is 3 feet. At $3 a foot, how much will Anna's flooring cost? (use 3.14 for π) (use area of a circle formula)

A = π × r² A = 3.14 × 3² A = 3.14 × 9 A = 28.26 the area of the elevator room is 28.26 feet 28.26 × $3 = $84.78 Anna's flooring will cost $84.78

area of a circle formula

A = π × r² π = ~3.14159 r = radius first, multiply the radius by the radius (which is r²) next, multiply the results by pi

David needs to buy wallpaper for his trapezoid shaped wall. The height is 10 feet, the bottom base is 8 feet, and the top base is 7 feet. At $0.50 a foot, how much will David's wallpaper cost? (use area of a trapezoid formula)

A= ½ × (b₁ + b₂) × h A= ½ × (7 + 8) × 10 A= ½ × (15) × 10 A= 75 the wall has an area of 75 feet 75 × $0.50 = $37.50 David's wallpaper will cost $37.50

area of a trapezoid formula

A= ½ × (b₁ + b₂) × h b₁ = base #1 b₂ = base #2 h = height first, the area of a trapezoid is found by adding b₁ and b₂ next, take the sum of the bases and multiply it by one half, then multiply it by the height

circumference of a circle formula

C = 2 × π × r π = ~3.14159 r = radius circumference of a circle is two multiplied by pi multiplied by the radius --------------- C = π × d π = ~3.14159 d = diameter use when the diameter of the circle is known diameter is two times the radius circumference of a circle is two multiplied by the diameter

Proportional? 3/4 = 8/10

NO

perimeter of a rectangle formula

P = (2 × l) + (2 × w) l = length w = width perimeter of a rectangle is the sum of all four sides two times the length plus two times the width (or you can just add all four sides together, end up with the same answer)

perimeter of a triangle formula

P = a + b + c perimeter of a triangle is the sum of all three sides

Proportional? 1/3 = 2/6

YES

Proportional? 3/12 = 1/4

YES

In a right triangle, if a=7 and b=4, what does c=? (use pythagorean theorem)

a² ⁺ b² = c² 7² ⁺ 24² = c² √(49 ⁺ 576) = √c² √625 = c 25 = c

pythagorean theorem formula

a² ⁺ b² = c² used to figure out the value of (mostly) the hypotenuse in a right triangle hypotenuse is represented as the side "c" in figure remember that the formula can only be applied to right triangles!

hypotenuse

the longest side of a right triangle, always across from the right angle