Algebra 1 - Solving Equations

One-Step Equations

100

Solve for b:

7 = b - 3

b = 10

200

Solve for x:

x/3 = 2

x = 6

WORK

x/3 = 2

x/3 *3 = 2 *3

x = 6

300

Solve for x:

5x = 20

x = 4

WORK

5x = 20

5x/5 = 20/5

x = 4

400

m/7 = 28

196

500

2.54 = p + 1.17

p = 1.37

Two-Step Equations

100

Solve for x:

2x + 3 = 15

x = 6

WORK

2x + 3 = 15

2x + 3 - 3 = 15 - 3

2x = 12

(2x)/2 = 12/2

x = 6

200

Solve for a:

0.5x + 5 = 18

x = 26

300

Solve for t:

5t + 8 = 93

t = 17

400

Solve for x:

(x – 7)/3 = 12

x = 43

500

12 = (x/7) + 3

x = 63

Writing Equations/expressions

100

I buy 16 bags of chocolate and there are y chocolates in each. Write an expression to show how many chocolates there are

16y

200

There are 82 students on every bus and then 8 students in one car. If there are b buses, how many students are there in total?

82b + 8

300

I have 396 pens. I divide them equally among x staff members and then give 13 away to students. How many do I have now?

396/x - 13

400

It costs 300kr to enter the theme park and then 23kr for every roller coaster you ride. You spend 484kr in total. Write an equation to represent this

300 + 23x = 484

500

The average age of 3 people is 5. The first two are 8 and 6. Write an equation to find the age of the last one. 

(8 + 6 + x) / 3 = 5

Substitution

100

3x.... if x=9

27

200

5y + 2....if y=7

37

300

1.25p + 8 ... if p=32

48

400

2(5x - 1)   if x = 12

118

500

9mn + 5 + 12m ... if m = 3 and n = 2

95

Word Problems

100

Solve:

Five friends equally split a restaurant bill that comes to $32.50. How much does each friend pay?

Each friend pays $6.50.

WORK

5x = 32.50

5x/5 = 32.50/5

x = 6.5 ~~~> $6.50

200

Solve:

You work for 4 hours on Saturday and 8 hours on Sunday. You receive a $50 bonus. You earn $164.00 total. How much did you earn per hour?

You earned $9.50 per hour.

WORK

4x + 8x + 50 = 164

12x + 50 = 164

12x + 50 - 50 = 164 - 50

12x = 114

12x/12 = 114/12

x = 9.5 ~~~> $9.50

300

Solve:

Two buildings have the same total height. One building has 8 floors with height, h. The other building has a ground floor of 16ft and 6 other floors with height, h. Write and solve an equation to find the height, h, of these floors.

8h = 16 + 6h
h = 8

WORK
8h = 16 + 6h
8h - 6h = 16 + 6h - 6h
2h = 16
2h/2 = 16/2
h = 8

400

Solve

Online concert tickets cost $37 each, plus a service charge of $8.50 per ticket. The Web site also charges a transaction fee of $14.99 for the purchase. You paid $242.49. How many tickets did you buy?

You bought 5 tickets.

WORK

37t + 8.50t + 14.99 = 242.49

45.5t + 14.99 = 242.49

45.5t + 14.99 - 14.99 = 242.49 - 14.99

45.5t = 227.5

45.5t/45.5 = 227.5/45.5

t = 5 ~~~> 5 tickets

500

Solve

Pristine Printing will print business cards for $0.10 each plus a setup charge of $15. The Printing Place offers business cards for $0.15 each with a setup charge of $10. What number of business cards costs the same from either printer? BONUS: What would the cost be?

Printing 100 cards would cost the same from either business.

WORK

0.10n + 15 = 0.15n + 10

0.10n - 0.10n + 15 = 0.15n - 0.10n +10

15 = 0.05n + 10

15 - 10 = 0.05n + 10 - 10

5 = 0.05n

5/0.05 = 0.05n/0.05

100 = n ~~~>100 cards

BONUS answer: It would cost $25.00 to make 100 cards from either place.

WORK

0.10n + 15 = ??

0.10(100) + 15 = 25 ~~~>$25.00

0.15n + 10 = ??

0.15(100) + 10 = 25 ~~~>$25.00