Notes 2-3: Applications of Equations
Objective: To write equations and solve word problems.
Geometry:
1. The width of a rectangle is three times its height. The area is 60.75 square feet. Find the dimensions.
Finance:
In Finance, interest is also known as return, yield, or profit.
2. A high risk stock pays dividends at a rate of 12% per year and a savings account pays 6% interest per year.
How much of the $9,000 investment should be put in a savings to obtain a return of 8% per year on the total
investment?
3. A real estate investment yields a return of 10% per year and a CD pays 6% interest per year. How much of
$7500 should be put in the real estate investment and how much should be put in the CD to obtain a return of
7% on the entire $7500?
Navigation:
4. A pilot wants to make an 840 mile round trip from Cleveland to Miami and back in 5 hours flying time.
There will be a headwind of 30 mph going to Miami, and it is estimated that there will be a 40 mph tailwind
returning to Cleveland. At what constant engine speed should the plane be flown?
5. A canoeist paddled a total of 11 hours on a 48 km round trip to Bear Lake. The upstream trip to bear lake
followed a period of heavy rain, and the current she paddled against was 3 km/hr. For the downstream return
trip, she paddled with the current that had slowed to 2 km/hr. At what speed could she paddle the canoe in still
water?
Mixture Problems:
6. A chemist has 30 mL of a 40% acid solution in a test tube. How much of the solution should be poured off
and replaced with pure acid so that the new mixture is 70% acid?
7. A car radiator contains 12 quarts of fluid, 20% of which is antifreeze. How much fluid should be drained
and replaced with pure antifreeze so that the resulting mixture is 50% antifreeze?