Proportions

Cross-multiplication

100

3/5=6/x

3x=30

200

n+7/7=4/9

n=-35/9

300

8/10=a+1/3

a=7/5

400

4/3=p+6/8

p=14/3

Direct proportions

100

120/360=S/900

S=300

200

$72/6 hours=$12 per hour

$168

300

8/75=F/240

25.6 liters

400

H/9=4/3

H=12

Indirect

100

A car takes 4 hours to reach a destination while traveling at 60 mph. How long will the trip take if the car travels at 80 mph?

3 hours.

200

A team of 2 workers can paint a house in 9 hours. How long would it take 6 workers to do the same job?

3 hours.

300

If 1 person takes 7 days to pick the pears from a tree, how many days will it take 7 people to do the same job?

1 Day.

400

If 10 people take 10 days to pick the apples from a tree, how many days will it take 4 people to do the same job?

25 Days.

Word problems

100

A cookie recipe for 16 cookies requires \(2\) cups of flour. How many cups of flour are needed to make 40 cookies?

x=5

200

A hiker walks 10 miles in 4 hours. If they keep walking at the same pace, how long will it take them to hike 18 miles?

x=7.2 hours

300

You can buy 4 bulbs of garlic for $8. How many bulbs can you buy for $32?

x=16

400

A 3-foot-tall child casts a 7-foot shadow on the ground. At the same time of day, how tall is a tree that casts a 14-foot shadow?

x=6