1. The document provides examples on how to solve proportion problems by determining quantities from a given proportion. It shows working through two examples, finding 3m - 2n : 3m + n given m:n = 4:3 and finding 4g + h : 8g + h given g:h = 4:3. 2. The examples demonstrate setting up equivalent fractions using the given proportions, then simplifying and solving to determine the ratios of the indicated quantities. 3. Additional practice problems are provided at the end to find ratios involving y and s from a given equation, and to solve for x from a given proportion.

1. Solving Problems
Involving Proportion

2. Examples on how to determine indicated
quantities from a given proportion.
1. If m:n = 4:3, find 3m – 2n : 3m + n
𝑚
𝑛
=
4
3
3𝑚−2𝑛
3𝑚+𝑛
=
3
4𝑛
3
−2𝑛
3
4𝑛
3
+𝑛
3m = 4n
4𝑛−2𝑛
4𝑛+𝑛
=
2𝑛
5𝑛
=
2
5
m=
4𝑛
3
Therefore,
Using m=
4𝑛
3
3m – 2n : 3m + n = 2:5

3. Example
1. If m:n = 4:3, find 3m – 2n : 3m + n
3𝑚−2𝑛
3𝑚+𝑛
=
3𝑚−2(
3𝑚
4
)
3𝑚+(
3𝑚
4
)
=
3𝑚−
3𝑚
2
3𝑚+
3𝑚
4
=
6𝑚−3𝑚
2
12𝑚+3𝑚
4
=
3𝑚
2
15𝑚
4
=
3𝑚
2
∙
4
15𝑚
=
12𝑚
30𝑚
=
2𝑚
5𝑚
=
2
5
Therefore, 3m – 2n : 3m + n = 2:5
𝑚
𝑛
=
4
3
4n = 3m
n=
3𝑚
4
using n =
3𝑚
4

4. Example
2. If g : h = 4 : 3, evaluate 4g + h : 8g + h
4𝑔+ℎ
8𝑔+ℎ
=
4
4ℎ
3
+ℎ
8
4ℎ
3
+ℎ
=
16ℎ
3
+ℎ
32ℎ
3
+ℎ
=
16ℎ+3ℎ
3
32ℎ+3ℎ
3
=
19ℎ
3
35ℎ
3
=
19ℎ
3
∙
3
35ℎ
=
19ℎ
35ℎ
=
19
35
Therefore, 4g + h : 8g + h=19:35
𝑔
ℎ
=
4
3
3g = 4h
g =
4ℎ
3
using g =
4ℎ
3

5. Example
2. If g : h = 4 : 3, evaluate 4g + h : 8g + h
4𝑔+ℎ
8𝑔+ℎ
=
4𝑔+
3𝑔
4
8𝑔+
3𝑔
4
=
16𝑔+3𝑔
4
32𝑔+3𝑔
4
=
19𝑔
4
35𝑔
4
=
19𝑔
4
∙
4
35𝑔
=
19𝑔
35𝑔
=
19
35
Therefore, 4g + h : 8g + h=19:35
𝑔
ℎ
=
4
3
4h = 3g
h =
3𝑔
4
using h =
3𝑔
4

6. Seatwork
Find
𝑦
𝑠
if 5y-2s:10 = 3y – s:7.

7. Seatwork
Solve for x in 5:4 = (3x+4):(5x-2)