Proportions and Scale Factor

Quiz 6B ReviewRatio, Unit Rate, and Conversion Factors

Solve each proportion. Show your algebraic steps.

a = 4 6 8

56 = a 7 2

Proportions

8a = 24 8 8 a = 3

7a = 1127 7

a = 16

Write a proportion. Show your algebraic steps. Tim can type 320 words in 2.5 minutes. Typing at

the same rate, how many data items can he input in 8 minutes?

◦ 320 = x 2.5 8

2.5x = 25602.5 2.5

X = 1024 words in 8 minutes.

Proportions

Write a proportion. Show your algebraic steps.

The height of a tree on a scale drawing is 6.5 in. The scale factor is 1:8. What is the actual height of the tree?

◦ 6.5 = 1 x 8

x = 52

The actual height of the tree is 52 inches.

Proportions

Write a proportion. Show your algebraic steps. A picture is 200 in. long and 510 in. tall. The

photographer is going to scale the picture so it is 800 in. long. To the nearest in., how tall is the new picture?

◦ 200 = 800 510 x

200x = 408000200 200

The height of the picture would be 2040 in. tall.

Proportions

If two cities are 15 inches apart on a map and in real dimensions they are 250 miles apart, what is the scale of the map?

◦ 15in = 3in . 250 miles 50 miles

Scale and Scale Factor

If two towns are 2 inches apart on a map and in real dimensions they are 10 miles apart, what is the scale of the map?

◦ 2in = 1in . 10 miles 5 miles

Scale and Scale Factor

What scale factor was used to build a 10 in. model of a 80 ft statue?

◦ 10in . 1ft . = 10 = 1 80 ft 12 in. 960 96

Scale and Scale Factor

Scale and Scale Factor

1 cm = 4.5 in

12 cm

24 cm 1 = 124.5 w

W = 54 in.

1 = 244.5 L

L = 108 in.

Scale and Scale Factor

1 cm = 8.5 in

18 cm

28 cm 1 = 18 8.5 w

W = 153 in.

1 = 288.5 L

L = 238 in.

The Cheetah can run at a top speed of 450 miles per hour. How many feet per second is this?◦ 450mi . 1hr . = 450mi . 5280 ft=2376000ft

= 1hr 3,600sec 3,600sec 1mi 3600sec

660ft/1sec

Scale and Scale Factor

The ape can swing at a top speed of 50 miles per hour. How many feet per second is this?◦ 50mi . 1hr . = 50mi . 2500 ft= 125000ft = 1hr 3,600sec 3,600sec 1mi 3600sec

34.72ft/1sec

Scale and Scale Factor

Dennis paid $276.25 for 3 tickets to see the Phillies. Express this as a unit rate.

◦ $276.25 = $92.08 3 tickets 1 ticket

Scale and Scale Factor

A 84-oz container of soda costs $4.72. At what price should a 144-oz container be sold in order for the unit rate for both containers to be the same?

◦ $4.72 = $.06 84 oz 1 oz

$.06 x 144 oz = $8.64

Scale and Scale Factor