Applications of Applications of EquationsEquations

Lesson 2.3Lesson 2.3

What are we doing?What are we doing?

Basically, everything we learned Basically, everything we learned in the previous two lessons will in the previous two lessons will be applied to real world be applied to real world situations or unique situations situations or unique situations that will call upon our newly that will call upon our newly gained knowledgegained knowledge

ExampleExample

The average of two real The average of two real numbers is 39.625, and one numbers is 39.625, and one number is 1500 times the number is 1500 times the reciprocal of the other. Find the reciprocal of the other. Find the two numbers.two numbers.

Yet another exampleYet another example

The width of a rectangle is three The width of a rectangle is three times its height. If it has an area times its height. If it has an area of 60.75 square feet, what are of 60.75 square feet, what are its dimensions?its dimensions?

Example Number 3Example Number 3

A storage locker in A storage locker in the shape of a the shape of a rectangular prism with rectangular prism with a square floor has a a square floor has a volume of 70,000 volume of 70,000 cubic inches. If the cubic inches. If the surface area of the surface area of the four walls and the top four walls and the top is 10,000 square is 10,000 square inches, what are the inches, what are the dimensions of the dimensions of the locker?locker?

I = PRT {Simple Interest}I = PRT {Simple Interest}

I I Interest {fee paid for use of Interest {fee paid for use of money}money}

P P Principal {amount put in} Principal {amount put in} r r rate {annual interest rate} rate {annual interest rate} t t time {represented in years} time {represented in years}

ExampleExample

A real estate investment yields a A real estate investment yields a return of 10% per year and a return of 10% per year and a certificate of deposit (CD) pays certificate of deposit (CD) pays 6% interest per year. How 6% interest per year. How much of $7500 should be put in much of $7500 should be put in the real estate investment and the real estate investment and how much should be put in the how much should be put in the CD to obtain a return of 7% on CD to obtain a return of 7% on the entire $7500?the entire $7500?

Example…again?Example…again?

A pilot wants to make an 840 A pilot wants to make an 840 mile round trip form Cleveland to mile round trip form Cleveland to Peoria and back in 5 hours Peoria and back in 5 hours flying time. There will be a flying time. There will be a headwind of 30 mph going to headwind of 30 mph going to Peoria, and it is estimated that Peoria, and it is estimated that there will be a 40-mph tailwind there will be a 40-mph tailwind returning to Cleveland. At what returning to Cleveland. At what constant engine speed should constant engine speed should the plane be flown?the plane be flown?

All about the examplesAll about the examples

A car radiator contains 12 quarts A car radiator contains 12 quarts of fluid, 20% of which is of fluid, 20% of which is antifreeze. How much fluid antifreeze. How much fluid should be drained and replaced should be drained and replaced with pure antifreeze so the with pure antifreeze so the resulting mixture is 50% resulting mixture is 50% antifreeze?antifreeze?

Last One, I promise!Last One, I promise!

A container in the shape of a A container in the shape of a rectangular prism with no top rectangular prism with no top that has a volume of 650 cubic that has a volume of 650 cubic inches is to be constructed from inches is to be constructed from a 28 x 20 inch piece of sheet a 28 x 20 inch piece of sheet metal by cutting squares of metal by cutting squares of equal size from each corner and equal size from each corner and folding up the flaps. What size folding up the flaps. What size square should be cut from each square should be cut from each corner?corner?