1. Math Project Josh Gustavus Candyce Cooley Michael Lipsey Craig Wright

2. The Problem… ► A militia preparing for a raid needs 2328 lbs. of gun powder with an ignition rate of 40%. ► Before they could carry out their operation, their base was raided and 1028 lbs. of their pre mixed gunpowder was taken. ► The militia was left with 1300 lbs. of gun powder with an ignition rate of 40% and they also had gun powder with an ignition rate of 20%.

3. The Solution… ► In order to get the 20% back to the 40%, they need, they had to re-supply and use some of the 70% ignition rate from their home base to mix.

4. The Formula… ► The militia has 1300 lbs. of gun powder left and needs a total of 2328 lbs. so they need to mix 1028 lbs. ► To find out how many pounds of each percent they need you use the equation X+Y=1028 ► Sense the desired rate of the mixture needs to be 40% and the two available batches of gunpowder have ignition rates of 70% and 20% the second equation will be.70x+.20y=1028(.40)

5. How to solve… ► For these types of problems there are two ways to solve them you can use either the Substitution Method or the Elimination Method. ► For this project we will show both methods

6. Elimination Method… ► First we multiply our second equation by 10 to get rid of decimals leaving us with 7x+2y=4112 ► Next we multiply our first equation by -2 and subtract the solution from are second problem. ► -2(x+y=1028) this gives us (-2x-2y= -2056) -(7x+2y= 4112) -(7x+2y= 4112)-5x=-2056 ► If we then divide both sides by -5 we can figure out that x=411.2

7. Elimination Method… ► If we take the 411.2 and plug it in for x in the equation x+y=1028 we can then solve for y. ► 411.2+y=1028 ► Subract 411.2 from both sides and we have y=616.8

8. Substitution method… ► For this method we take the same two formulas x+y=1028 and 7x+2y=4112 ► First we need to isolate a variable in the first equation by subtracting y from both sides to get x=1028-y ► Next we substitute that solution into the second equation giving us 7(1028-y)+2y=4112 ► Distribute the seven 7196-7y+2y=4112 then combine like terms to get 7196-5y=4112

9. Substitution method… ► Next we subtract 7196 from both sides leaving us with -5y=-3084 ► Finally we dived both sides by -5 and learn that y=616.8 ► Now we can take that information and plug it in to the first problem and have x+616.8=1028 ► So x=411.2

10. Conclusion… ► So in order for the militia to get its gunpowder supply back to the full 2328 pounds needed, with an ignition rate of 40%, they must mix together 411.2 pounds of powder with an ignition rate of 70% and 616.8 pounds of powder with an ignition rate of 20%

11. Class Problem… ► Lets say instead of needing 2328 lbs of gunpowder with an ignition rate of 40% they need 1750 lbs. of gun powder with an ignition rate of 70%. ► 735 lbs of their powder was taken. ► In their storage they have powder with an ignition rate of 80% and an ignition rate of 30% ► How much of each type of gun powder do they need to mix to be back at 1750 lbs. of gun powder with an ignition rate of 70%

12. The Answer… ► 203 lbs of gun powder with an ignition rate of 80% ► 812 lbs. of gun powder with an ignition rate of 30%