mixing paint
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Mixing Paint. Rational Equations. Paint Mixing. - PowerPoint PPT PresentationTRANSCRIPT
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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%.