### Proportions and Scale Factor

```Quiz 6B Review
Ratio, Unit Rate, and Conversion Factors
Solve each proportion. Show your algebraic steps.


a = 4
6
8
8a = 24
8
8
a=3
56 = a
7
2
7a = 112
7
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 = 2560
2.5
2.5
X = 1024 words in 8 minutes.
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.
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 = 408000
200
200
The height of the picture would be 2040 in. tall.

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
=
250 miles
3in .
50 miles

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
=
10 miles
1in .
5 miles

What scale factor was used to build a 10 in.
model of a 80 ft statue?
◦
10in
80 ft
.
1ft . = 10 =
12 in.
960
1
96
1 = 12
4.5
w
W = 54 in.
24 cm
12 cm
1 = 24
4.5
L
L = 108 in.
1 cm = 4.5 in
1 = 18
8.5
w
W = 153 in.
28 cm
18 cm
1 = 28
8.5
L
L = 238 in.
1 cm = 8.5 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

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

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

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
```