1. Using Systems of Equations
Objectives:
To solve problems using systems of equations

2. Example 1 Translate into a system of equations and solve.
The Yellow Bus company owns three times as many mini-buses as regular buses. There are 60 more mini-buses than regular buses. How many of each does Yellow Bus own?
Let m be the number of mini-buses
Let r be the number of regular buses
m = 3r
m =
r + 60
m = 3r
3r = r + 60
2r = 60
m = 3(30)
r = 30
m =90
30 regular buses, 90 mini-buses

3. Practice Translate into a system of equations and solve.
An automobile dealer sold 180 vans and trucks at a sale. He sold 40 more vans than trucks. How many of each did he sell?

4. Example 2 Translate into a system of equations and solve.
Bob is 6 years older than Fred. Fred is half as old as Bob. How old are they?
Let b be the age of Bob
Let f be the age of Fred
b =
f + 6
b = f + 6
b = 2f
f + 6 = 2f
b = (6) + 6
6 = f
b = 12
Bob is 12.
Fred is 6.

5. Example 3 Translate into a system of equations and solve.
Fran is two years older than her brother. Twelve years ago she was twice as old as he was. How old are they now?
age now
age 12 years ago
Fran
brother f
f - 12 b
b - 12
f =
b + 2
b = 14
f – 12 =
2(b – 12)
f = b + 2
(b + 2) – 12 = 2(b – 12)
f =
f = 16
b – 10 = 2b – 24
b = 2b – 14
Fran is 16; brother is 14

6. Practice Translate into a system of equations and solve.
Wilma is 13 years older than Bev. In nine years, Wilma will be twice as old as Bev. How old is Bev?