Download Ratios and Proportions

Ratios and Proportions
Warm Up - Simplify
a ) 108  6 3
b
11

2
c)
3
21

7
21
22
2
Ratio – comparison of two
numbers by division.
Proportion – an equation
stating that two ratios are
equal.
Ratio
# boys to # girls
# boys : # girls
# boys
# girls
Ratios are equal if the cross
products are equal.
24 4

30 5
Check :
24 x 5  30 x 4
120  120
n 24

Solve 15 16
n 24

15 16
16n  (24)(15)
16n  360
16n 360

16
16
n  22.5

 Or

45 

2 
3x  1 x
Solve

5
7
3x  1 x

5
7
(7)(3 x  1)  5 x
21x  7  5 x
16 x  7
7
x
16
8
3
Solve

4x  1 2x  5
8
3

4x  1 2x  5
8(2 x  5)  3(4 x  1)
16 x  40  12 x  3
4 x  37
37
x
4
Seth earns $152 in 4 days. At that rate, how
many days will it take him to earn $532?
152 532

4
x
152 x  4(532)
152 x  2128
x  14 days
Lanett drove 248 miles in 4 hours. At that rate,
how long did it take her to drive 93 miles?
248 (93)

4
x
248 372

4
x
248 x  4(372)
248 x  1488
x  1.5 hours
A blueprint for a house states that 2.5 inches
equals 10 feet. If the length of a wall is 12 feet,
how long is the wall on the blueprint?
2.5 in.
x

10 ft. 12 ft
10 x  (2.5)(12)
10 x  30
x  3 inches
The ratio of the measures of the angles of a
triangle is 2 :7 : 3. Find the measure of the
smallest angle of the triangle.
 Smallest Angle:
2 x  7 x  3x  180
12 x  180
x  15
2x
2(15)  30

The profits in a business are shared by three partners in the ratio 4 : 5 : 9.
The profits for the year was $720,000. Determine the number of dollars
received by the partner with the second largest share.

Find x:
4 x  5 x  9 x  720,000
18 x  720,000
x  40,000

Find the 2nd largest
shared holder’s
profit:
5x
5( 40,000)
$200,000
The ratio of the measures of the angles of a triangle is 3
: 4 : 2. Find the measure of the largest angle of the
triangle.

Find x:

The largest angle:
3x  4 x  2 x  180
4x
9 x  180
4( 20)
x  20
80

If the ratio of boys to girls in a geometry class is 3:1, and
there are 28 students in the class, how many are boys?

Find x:
3x  x  28
4 x  28
x7

Find the number of
boys.
Boys : 3x
3(7)  21 Boys
The width of a rectangle is 3/5 of the length. The
perimeter is 48 feet. Find the area of the rectangle.
3
w l
5
2l  2 w  P
3
2l  2 l  48
5
6
2l  l  48
5
10l  6l  240
16l  240
l  15 ft.
Area  lxw
3

A  15  15 
5

A  15(9)
A  135 sq. ft.