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Mixing Paint

Rational Equations

+Paint Mixing1) 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 PercentOf yellowIn 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?

3. 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?

ExtensionWrite a problem that can be solved by using a rational equation.

Use cross products to solve it.

Solutions1. Ans: y= 18 pints

2. Ans: y= 12 pints

3. Ans: y= - 4.5 pints (this works mathematically but not in the real world)

So we should solve for blue

Ans: b= 18 pints4. Ans: 20 pints of yellow5. 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%.