1. UNIT 1: FOUNDATIONS OF ALGEBRA
LEARNING TARGET:
I can solve applied arithmetic problems using appropriate units.

2. 1.6: Applications Using Units, Rates and Proportions
Applications of units, rates, proportions and percentages are likely the most frequently used and most practical applications of mathematics encountered in every day life. We present a few common examples of these applications with an emphasis on how appropriate use of units can help us solve problems of this kind and achieve a deeper understanding of them.

3. EXAMPLE:
Example 1. A large screen TV is that originally sells for $900 is marked down to $684. What is the percentage decrease in the price?

4. 𝑂𝑅𝐼𝐺𝐼𝑁𝐴𝐿 𝑃𝑅𝐼𝐶𝐸−𝑁𝐸𝑊 𝑃𝑅𝐼𝐶𝐸 𝑂𝑅𝐼𝐺𝐼𝑁𝐴𝐿 𝑃𝑅𝐼𝐶𝐸 ∗100
RATE OF CHANGE
𝑂𝑅𝐼𝐺𝐼𝑁𝐴𝐿 𝑃𝑅𝐼𝐶𝐸−𝑁𝐸𝑊 𝑃𝑅𝐼𝐶𝐸 𝑂𝑅𝐼𝐺𝐼𝑁𝐴𝐿 𝑃𝑅𝐼𝐶𝐸 ∗100
900− ∗100= ∗100= ?

5. APPLYING PERCENTS TO PRICES
Example 2. Tom, Dick and Harry are friends who go shopping. Tom buys a shirt for $25, Dick buys a shirt for 15% more than Tom’s shirt, and Harry buys a shirt for 20% more than Dick’s shirt. What was the combined cost of all three shirts?

6. RATE OF CHANGE
Example 3. (a) A man making an annual salary of $80,000 per year gets laid off and is forced to take a part- time job paying 60% less. What is the annual salary for his part-time job?

7. CREATING AN EQUATION
(b) Suppose the man is making x dollars per year instead of $80,000. What is the annual salary for his part-time job in terms of x ?

8. PROPORTIONS: EXAMPLE
Example 4. A group of students take a van to a football game. They average 20 miles per gallon on the 155-mile trip. How many gallons of gas do they use?

9. CONVERSION RATES
Example 5. A car is going 66 feet per second. How fast is the car going in miles per hour?

10. CONVERSION RATES
Solution. The relationship among the units involved in this problem is more complicated than in Example 4. This relationship has the template:
feet sec × sec hour × miles feet = miles hour

11. DISTANCE
Example 6. Romeo and Juliet have a lover’s quarrel. Juliet bolts away due east at 5 feet per second. One minute later, Romeo stomps off in the opposite direction at 4 feet per second. How far apart are they 3 minutes after Juliet leaves?

12. DISTANCE 180 sec = 3 min× 60 sec min 5 feet sec ×180 sec = 900 feet
Solution. We break down this problem into two parts by calculating the distance that Juliet travels and adding it to the distance Romeo travels. Juliet travels 3 minutes and we first convert that into seconds.
180 sec = 3 min× 60 sec min
5 feet sec ×180 sec = 900 feet
Juliet travels 900 feet. How far does Romeo travel, using the same process?
What is the total distance?

13. PROPORTIONS: DOSAGES
Example 7. The recommended dose of a certain drug to be given to a patient is proportional to the patient’s weight. If 2 milligrams of the drug is prescribed for someone weighing 140 pounds, how many milligrams should be prescribed for someone weighing 180 pounds? Round your answer to the nearest hundredth of a milligram.

14. COMPARING SALARY
Example 8. Jack and Jill both work part-time at a local Burger Barn.
(a) Jack makes $2 per hour less than Jill and he works 5 hours more than Jill during one week. If Jack makes $7 dollars per hour and works 22 hours, how much do Jack and Jill combined make (in dollars) that week?
(b) Jack makes r dollars per hour less than Jill and he works h hours more than Jill during one week. If Jack makes $7 dollars per hour and works 22 hours, how much do Jack and Jill combined make (in dollars) that week in terms of r and h ?