Page 207 - Algebra 1

Proportions are used to represent many real-world situations that require finding a missing value. Using the cross products is an efficient method for solving the proportions.
Solving Multi-Step Proportions
a. The ratio of boys to girls in a math class is 3:2. The class has
25 students in all. How many boys and how many girls are in the class?
SOLUTION
Example
4
Math Reasoning
Analyze Would you get the same answer for Example 4a if your ratio compared girls to the total group? Explain.
The ratio of boys to girls is 3 to 2. There are 3 boys in each group of 5 students.
__
number of boys = 3 Write a ratio.
_ total in group 5
Write and solve a proportion. Let b represent the number of boys in the class.
_3 = _b 5 25
3 · 25 = 5 · b 5b = 75
There are b boys to 25 students.
Write the cross products. Simplify.
Solve.
b = 15
There are 15 boys in the class. So, there are 25 - 15 or 10 girls in the class.
b. On the map, Albany to Jamestown measures 12.6 centimeters, Jamestown to Springfield measures 9 centimeters, and Springfield to Albany measures 4.75 centimeters. What is the actual distance from Albany to Jamestown to Springfield and back to Albany?
12.6 + 9 + 4.75 = 26.35 cm 26.35 cm = 1 cm
__
x km 25 km
26.35 · 25 = 1 · x 658.75 = x
Albany
SOLUTION
Springfield
Scale: 1 cm:25 km
Find the total distance on the map.
Set up a proportion using the map scale.
Write the cross products. Solve.
The actual distance is 658.75 kilometers.
Proportions are frequently used to solve problems involving variations of the
Jamestown
192 Saxon Algebra 1
distance formula d = rt.
rate=distance or time=distance
__ time rate