Algebra 1 - Solving Equations

Riddles

100

You are in a race and in 8th place. You keep running and pass the person in 2nd place. What place are you in now?

2nd place 

200

How can you go 10 days without sleep?

Sleep at night

300

What has 13 hearts, but no lungs or a stomach?

A deck of cards

400

This vehicle is spelt the same way from the front as well as the back. 

What is a racecar?

500

I am an odd number, take away a letter and I become even. 

What is seven?

Angle Relationships

100

The equation 30 + x = 90 shows this relationship.

What is complementary or right angle?

200

Two angles are supplementary. The first angle has a value of (2x+ 10) and the second angle is 40. Solve for x. 

What is 65?

300

This angle has a degree measure that is greater than 90 and less than 180.

What is an obtuse angle?

400

2x + 6 = 3x shows two angles that are congruent because they are across from each other and this relationship

What is vertical angles?

500

Two angles are across from one another on a vertical angle set. One angle is (5x+25), the angle across in the opposite direction from the first angle is (2x-11)

x=-12

Random Trivia

100

These are two number that go together. Saying these numbers will make you cringe or laugh. 

What is 6/7?

200

The year that Yuma High School was founded.

What is 1909?

300

The most popular Youtuber in 2024.

Who is Mr. Beast?

400

This player won the Golden Ball in the 2022 World Cup.

Who is Lionel Messi?

500

These are all of the questions on the rainbow. 

Red

Orange

Green

Blue

Indigo

Violet

Variables on Both Sides

100

Solve for b:

3b - 4 = b + 2

b = 3

WORK
3b - 4 = b + 2
3b - 4 + 4 = b + 2 + 4
3b = b + 6
3b - b = b - b + 6
2b = 6
2b/2 = 6/2
b = 3

200

Solve for x:

5x + 2 = 2x + 14

x = 4

WORK
5x + 2 = 2x + 14
5x + 2 - 2 2x + 14- 2
5x = 2x + 12
5x - 2x = 2x - 2x + 12
3x = 12
3x/3 = 12/3
x = 4

300

Solve for p:

1.5p = 1.25p + 8

p = 32

WORK
1.5p = 1.25p + 8
1.5p - 1.25p = 1.25p - 1/25p + 8
0.25p/0.25 = 8/0.25
p = 32

400

Solve for x:

2(5x - 1) = 3(x + 11)

x = 5

WORK
2(5x - 1) = 3(x + 11)
10x - 2 = 3x + 33 [Distribute]
10x - 3x - 2 = 3x - 3x + 33
7x - 2 + 2 = 33 + 2
7x/7 = 35/7
x = 5

500

Solve for x:

9m - 4 = -3m + 5 + 12m

NO SOLUTION
-4 = 5

WORK
9m - 4 = -3m + 5 + 12m
9m - 4 = -3m + 12m + 5
9m -9m - 4 = 9m -9m + 5
-4 = 5 <~~~NO! So, No Solution!

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