+ Mixing Paint Rational Equations

+ Paint Mixing 1) You have a 12 pint mixture of paint that is made up of equal amounts of blue paint and yellow paint. You need to create a special shade of green for your art class project. The special shade of green is 80% yellow. How many pints of yellow paint do you need to add to the mixture? Solve this problem by using a rational equation. Start with a verbal model. Now use Cross-Products to solve. Pints of yellow paint in mixture +Pints of yellow paint needed ______________________________________________ Pints of paint in mixture +Pints of yellow paint needed = Desired Percent Of yellow In mixture

+ Use a Rational Equation. 2. What if you needed a paint mixture that is 75% yellow? How many pints of yellow paint would you need to add to the mixture? 2. What if you needed a paint mixture that was 20% yellow? How many pints of yellow paint would you need to add? What is the problem with this answer? What is another way to approach this problem and create a mixture that is 20% yellow by still using a rational equation?

+ Other methods to solve the paint mixture problem. Use a different method to solve the following mixture problem. 4. You have a mixture of paint that is made up of 4 pints of yellow and 8 pints of blue paint. How many pints of yellow need to be added to get a 75% yellow mixture? 5. What if we wanted a 50% mixture? Now that you have tried different methods, which do you prefer and why?

+ Use rational equations to solve the following problems. 6. Batting average is calculated by dividing the number of hits by the number of times at bat. A player has been at bat 90 times and has a batting average of.200. How many consecutive hits would the player need to raise the average to.250? 7. A basketball player has made 40% of 30 free throw attempts so far. How many consecutive free throws must he make to raise his percent to 50? To 60?

Extension Write a problem that can be solved by using a rational equation. Use cross products to solve it.

Solutions 1.Ans: y= 18 pints 2.Ans: y= 12 pints 3.Ans: y= pints (this works mathematically but not in the real world) So we should solve for blue Ans: b= 18 pints 4.Ans: 20 pints of yellow 5.Ans: 4 pints of yellow

Solutions (continued) 6.Let x = original number of hits substitute x = 18 into proportion Let h = number of Additional hits Ans: h = 6 more hits 7.Ans: 6 consecutive free throws for 50% and 15 consecutive free throws for 60%.