Equations Review

Proportions

100

x/5=6/10

x=4

200

3/x=15/22

x=4.4

300

(x-3)/9=18/36

x=7.5

400

(x+9)/(x-5)=2/9

x=-13

500

3/10=(x-2)/(x+6)

x=5.43

Distributive Property

100

2(x-1)=8

x=5

200

4(x+10)-2=42

x=1

300

5(x-2)=-10

x=0

400

5(2x-12)=-100

x=-4

500

5(x+6)-(4x+7)=26

x=3

Combining Like terms

100

4x+5-12=26

x=8

200

2x+7x=72

x=8

300

-4x+3-1+9x=57

x=11

400

-6x+13-8x+2=-83

x=7

500

-x+17+14x-1=-29.5

x=-3.5

Variables on both sides

100

2x+4=3x

x=4

200

-3x-10=-8x

x=2

300

5x=5x+8

No Solution

400

3(2x-5)=-2x-36.6

x=-2.7

500

4(2x-7)=-(-7x+5)+x-23

All Real Numbers

Word Problems

100

Set Up (don't solve) a proportion that represents this situation. If Mark can run 3 miles in 24 minutes, how long will it take him to run 5 miles?

Multiple Answers

example: 3/24=5/x

200

If you can buy 4 books for $10, how many books could you buy with $15?

6 books

300

The school takes a field trip to the Shedd Aquarium. If there are 203 people going and the school paid $2334.50 total, how much did each ticket cost?

$11.50

400

Uber charges $2 per mile along with a $3 base fee for your ride. Lyft charges $2.50 per mile but has no base fee for rides. How many miles would you need to be driving for it to cost the same amount to take an Uber or a Lyft?

6 miles

500

Normally, it takes me 40 minutes to drive to work. Today, I started driving, and drove 4 miles, but I realized I forgot something so I had to turn around and drive 4 miles back. Total, this added 8 miles to my trip and it took me 55 minutes to get to work instead of 40. How many miles is my normal trip?

21.33 miles