1. Warm–up #3 1. Find two consecutive integers whose product is 756. 2. If $7000 is invested at 7% per year, how much additional money needs to be invested at 14% per year so that the total annual interest income from the investments is $1750?

2. Warm–up #3 Solutions 1. Find two consecutive positive integers whose product is 210. 1 st # = x2 nd # = x + 1 x(x + 1) = 210 x 2 + x – 210 = 0 (x + 15)(x – 14) = 0 x = –15, 14 14 & 15

3. Warm–up #3 Solutions 2. If $7000 is invested at 7% per year, how much additional money needs to be invested at 14% per year so that the total annual interest income from the investments is $1750? PrincipalratetimeInterest Inv 1 Inv 2 Total 7000 + x 7000 x.07.14 1 1 = 7000(.07) = 490.14x 1750 equation! 490 +.14x = 1750

4. .14x = 1260 x = 9000 $9000 at 14% Warm–up #3 Solutions

5. Homework Log Tues 10/6 Lesson 2 – 2 Learning Objective: To solve mixture problems Hw: #204 Pg. 111 #17, 18, 21 – 26 all, redo 3, 5, 11

6. 10/6/15 Lesson 2 – 2 Mixture Problems Day 2 Advanced Math/Trig

7. Learning Objective To solve mixture problems

8. Mixture Solutions “Pure” Acid = 100% “Water” = 0%

9. Mixture 1. A chemist has 16L of a mixture that is 65% acid. How much of an 85% solution should she add to make a mixture that is 70% acid? Amount%Total Solution 1 Solution 2 Mix 70(x + 16) 65 x + 16 x 16 85 70 16(65) 85x Tells you it’s the mix 16(65) + 85x = 70(x + 16) =

10. Mixture Problem #1 cont’d 16(65) + 85x = 70(x + 16) 1040 + 85x = 70x + 1120 15x = 80 x = 5 1 / 3 L

11. Mixture 2. If the popcorn is worth $0.80 a pound & peanuts are worth $2.50 a pound, how much of each should go into the mixture for a 1-pound box that sells for $1.82 per pound? Amount$/eaTotal Popcorn Peanuts Mix 1.82 0.80 1 1 – x x 2.50 1.82.80x 2.50(1 – x).80x + 2.50(1 – x) = 1.82 =

12. Mixture Problem #2 cont’d.80x + 2.50(1 – x) = 1.82.80x + 2.50 – 2.50x = 1.82 –1.7x = –.68 x =.4 1 – x =.6.4 lb of popcorn.6 lb of peanuts

13. Mixture 3. 4 qt. of an acid solution was mixed with 6 qt of pure water to make an 8% acid solution. Find the % concentration of the first solution. Amount%Total Solution 1 Solution 2 Mix 80 x 10 6 4 0 8 4x 0 4x + 0 = 80 = 20%

14. Mixture 4. Hot Peanuts which cost $11/oz are made by combining peanuts that cost $7/oz with spices that cost $21/oz. How many oz of peanuts and spices are needed to make 7oz of Hot Peanuts? Amount$/eaTotal Peanuts Spices Hot Peanuts 77 7 7 7 – x x 21 11 7x 21(7 – x) 7x + 21(7 – x) = 77 =

15. Mixture Problem #4 cont’d 7x + 21(7 – x) = 77 7x + 147 – 21x = 77 –14x = –70 x = 5 7 – x = 2 5 oz of peanuts 2 oz of spices

16. Coin Problems 5. Suppose 21 nickels, dimes, & quarters are worth $2.45 & there are three times as many dimes as quarters. How many of each are there? Amount$/eaTotal Nickels Dimes Quarters Total.25x 0.05 x 3x 21 – 3x – x 0.10 0.25.05(21 – 4x).10(3x).05(21 – 4x) +.10(3x) +.25x = 2.45 = 21 2.45

17. Coin Problem #5 cont’d.05(21 – 4x) +.10(3x) +.25x = 2.45 5(21 – 4x) + 10(3x) + 25x = 245 105 – 20x +30x + 25x = 245 35x = 140 x = 4 3x = 12 21 – 4 – 12 = 5 5 Nickels, 12 Dimes, & 4 Quarters

18. Ticket Out the Door Paula wants to make 15 gal. of 57% acid solution by mixing together a 65% acid solution and a 55% acid solution. How much of each solution must she use?

19. Homework #204 Pg. 112 17, 18, 21 – 26 all & RE-DO 3, 5, 11 “Pure” acid  100% “Water”  0%