9th Grade Algebra

unit 1

100

1. A rectangle has a length that is 33 times its width. If the perimeter of the rectangle is 4848 units, what are the length and width of the rectangle?

1. Let the width be xx, so length is 3x3x. Perimeter: 2(x+3x)=482(x+3x)=48
   2(4x)=482(4x)=48
   8x=488x=48
   x=6x=6
   Width: 66 units, Length: 1818 units

200

1. Jamie has twice as many dimes as nickels, and together they total . How many dimes and how many nickels does Jamie have?

Let number of nickels be nn, dimes 2n2n.
0.05n+0.10(2n)=3.300.05n+0.10(2n)=3.30
0.05n+0.20n=3.300.05n+0.20n=3.30
0.25n=3.300.25n=3.30
n=13.2n=13.2

300

 A car travels 120120 kilometers in 22 hours at a constant speed. If the car continues at this speed, how far will it travel in 55 hours?

Speed =1202=60=2120=60 km/h
Distance in 55 hours: 60×5=30060×5=300 km

400

The sum of three consecutive integers is 7272. What are the integers?

Let the integers be x,x+1,x+2x,x+1,x+2:
x+(x+1)+(x+2)=72x+(x+1)+(x+2)=72
3x+3=723x+3=72
3x=693x=69
x=23x=23
Integers: 23,24,2523,24,25

500

1. The area of a triangle is 5454 square units, and its base is 99 units. What is the height of the triangle?

1. Area formula: 12×base×height=5421×base×height=54
   12×9×h=5421×9×h=54
   4.5h=544.5h=54
   h=12h=12 units

unit 2

100

1. A group of friends goes to a movie theater. Each ticket costs xx dollars. If they buy 55 tickets and spend a total of 4545 dollars, what is the value of xx?

1. x=9x=9

200

1. The length of a rectangle is 33 times its width. If the perimeter of the rectangle is 4848 units, what are the length and width of the rectangle?

1. Let width = ww, length = 3w3w, so 2(w+3w)=482(w+3w)=48
   w=6w=6, length = 1818, width = 66

300

1. Sarah wants to buy a new phone that costs 300300 dollars. She saves 2020 dollars each week. How many weeks will it take her to save enough money to buy the phone?

15 weeks 

400

1. A car travels 6060 miles in 1.51.5 hours at a constant speed. What is the car’s speed in miles per hours

40 miles per hour

500

1. The sum of three consecutive integers is 7272. What are the three integers?

1. 23,24,2523,24,25

unit 3

100

1. A rectangle has a length that is 33 times its width. If the perimeter of the rectangle is 4848 units, what are the length and width of the rectangle?

Let width be ww, length be 3w3w. Perimeter: 2(w+3w)=482(w+3w)=48 → 2(4w)=482(4w)=48 → 8w=488w=48 → w=6w=6. Length: 3×6=183×6=18. 

200

Maria bought 44 notebooks and 22 pens for . A notebook costs more than a pen. How much does each notebook and each pen cost?

Let the cost of a pen be xx. Then notebook is x+3x+3. Equation: 4(x+3)+2x=144(x+3)+2x=14 → 4x+12+2x=144x+12+2x=14 → 6x=26x=2 → x=13x=31.

300

1. A car travels 6060 miles in 1.51.5 hours at a constant speed. At this rate, how far will the car travel in 44 hours?

1. Rate: 601.5=401.560=40 miles/hour. In 44 hours: 40×4=16040×4=160 miles.
   Distance: 160160 miles.

400

1. The sum of three consecutive integers is 7575. What are the three integers?

1. Let integers be xx, x+1x+1, x+2x+2. x+(x+1)+(x+2)=75x+(x+1)+(x+2)=75 → 3x+3=753x+3=75 → 3x=723x=72 → x=24x=24.
   Integers: 24,25,2624,25,26.

500

1. A triangle has side lengths xx, x+2x+2, and x+4x+4. If the perimeter of the triangle is 3030 units, what is the length of each side?

1. x+(x+2)+(x+4)=30x+(x+2)+(x+4)=30 → 3x+6=303x+6=30 → 3x=243x=24 → x=8x=8.
   Sides: 88, 1010, 1212 units.

unit4

100

1. A rectangular garden has a length that is 33 meters longer than its width. If the perimeter of the garden is 3434 meters, what are the length and width of the garden?

1. Let width be xx, length is x+3x+3. 2x+2(x+3)=342x+2(x+3)=34 → x=7x=7 (width), x+3=10x+3=10 (length).

200

1. A cell phone plan charges per month plus for every text message sent. If a student’s monthly bill was , how many text messages did they send that month?

1. Let xx = number of texts. 20+0.10x=3520+0.10x=35 → 0.10x=150.10x=15 → x=150x=150 texts.

300

 car travels 180180 kilometers in 33 hours at a constant speed. How long will it take the same car to travel 300300 kilometers at the same speed?

1. Speed is 180÷3=60180÷3=60 km/h. 300÷60=5300÷60=5 hours.

400

1. The sum of three consecutive integers is 7272. What are the three integers?

1. Let integers be x,x+1,x+2x,x+1,x+2. x+x+1+x+2=72x+x+1+x+2=72 → 3x+3=723x+3=72 → 3x=693x=69 → x=23x=23. Integers: 23,24,2523,24,25.

500

1. A concert hall sold 500500 tickets for a show. Adult tickets cost each and student tickets cost each. If the total revenue was , how many adult tickets and how many student tickets were sold?

1. Let xx = adult tickets, 500−x500−x = student tickets. 15x+10(500−x)=630015x+10(500−x)=6300 → 15x+5000−10x=630015x+5000−10x=6300 → 5x=13005x=1300 → x=260x=260 adults, 500−260=240500−260=240 students.

unit 5

100

1. A rectangle has a length that is twice its width. If the perimeter of the rectangle is 3636 units, what are the dimensions of the rectangle?

1. Let the width be xx. Then the length is 2x2x. Perimeter: 2x+2(2x)=362x+2(2x)=36, so 2x+4x=362x+4x=36, 6x=366x=36, x=6x=6. Width: 66 units; Length: 1212 units.

200

1. Jamie is shopping for school supplies. She buys 33 notebooks at each, 22 packs of pencils at each, and one binder for . How much does Jamie spend in total?

1. Notebooks: 3×2=63×2=6; Pencils: 2×1.5=32×1.5=3; Binder: 44. Total: 6+3+4=136+3+4=13. Jamie spends .

300

the sum of three consecutive integers is 7272. What are the integers?

let the first integer be xx. Then x+(x+1)+(x+2)=72x+(x+1)+(x+2)=72; 3x+3=723x+3=72; 3x=693x=69; x=23x=23. The integers are 23,24,2523,24,25.

400

1. A train travels 6060 miles in 1.51.5 hours. What is the average speed of the train in miles per hour?

1. Average speed = 601.5=401.560=40 miles per hour.

500

1. A triangle has sides of lengths 77 cm, 2424 cm, and 2525 cm. Is the triangle a right triangle? Justify your answer.

1. Check if 72+242=25272+242=252: 49+576=62549+576=625, 625=625625=625. Yes, the triangle is a right triangle.