1. More applications of Linear Equations
Section 1.7
More applications of Linear Equations

2. Introduction to Problem Solving
Mathematical Modeling- The process of translating phrases or sentences into algebraic expressions or equations.
Verbal Model
Verbal Description
Algebraic
Equation

3. Total interest ($1,110) Interest earned at 8% Interest earned at 7%
Example 1: A professor has $15,000 to invest for one year, some at 8% and the rest at 7% . If she wants to earn $1,110 from these investments, how much should she invest at each rate?
Total
interest ($1,110)
Interest earned at 8%
Interest earned at 7%
VERBAL MODEL
i = p • r • t
8% investment
7% investment
.08x x
.08 1
.07(15,000 – x)
15,000 - x
.07 1
0.08x ( 15,000 – x ) = 1,110
ALGEBRAIC EQUATION

4. Example 1 (continued) 0.01x = 60 0.08x + 0.07(15,000 – x ) = 1,110
x = 6,000 Multiply both sides by 100
Therefore, $6,000 should be invested at 8% and $9,000 should be invested at 7%.

5. 55 mph 50 mph 157.5 miles Rockford Wausau
Example 2: A car leaves Rockford traveling toward Wausau at the rate of 55 mph. At the same time, another car leaves Wausau traveling toward Rockford at the rate of 50 mph. How long will it take them to meet if the cities are mile apart?
55 mph
50 mph
157.5 miles
Rockford Wausau

6. Rate x Time = Distance Faster car Slower car 55 t 55t 50 t 50t
VERBAL Distance of Distance of
MODEL faster car slower car =
Distance between the cities
Rate x Time = Distance
Faster car
Slower car 55 t
55t 50 t
50t
55t t =
105t =
t = 1.5 hrs.
ALGEBRAIC
EQUATION

7. Amt. fat in 12L of 4% Amt. fat in 1% milk Amt. fat in 2% mixture
Example 4: A container is partially filled with 12 liters of whole milk containing 4% butterfat. How much 1% milk must be added to get a mixture that is 2% butterfat?
VERBAL
MODEL
Amt. fat in L of 4%
Amt. fat in % milk
Amt. fat in % mixture
Amt of 4% milk = 12L Amt of 1% milk = x
Amt of fat in 4% milk = .04(12) Amt of fat in 1% milk = 0.01x
Amt of fat in mixture = 0.02(x + 12)
ALGEBRAIC (12) + .01x = .02(x + 12)
EQUATION

8. 48 + x = 2 (x + 12 ) Multiply both sides by 100 48 + x = 2x + 24
Example 4 (continued)
.04(12) x = 0.02 (x + 12 )
x = .02 (x + 12)
48 + x = 2 (x + 12 ) Multiply both sides by 100
48 + x = 2x + 24
x = 24
Therefore, 24 liters of 1 % milk should be added to get a mixture that is 2 % butterfat.