1. Money Problems: By Dr. Marcia Tharp and Dr. Julia Arnold

2. In money problems we encounter two types of numbers: For example, if we say “the number of coins is 6”, 6 represents how many coins. If we say the value of the coins is 60 cents, then 60 represents how much the coins are worth. The two ideas are: how many and value of See if you can pick out the the number for how many, and the number for the value of in the next problem.

3. Example 1 The Hurrah Players sold 600 tickets to a recent event. Adults paid $5 each and students paid $2 each. If the total collected was $2025, how many tickets of each type were sold? 600 is how many $5, $2, and $2025 represents the value of

4. If you have 5 nickels, what is the value of the money? 25 cents If you have $3.00 in dimes, how many dimes do you have? 30 How did you get the numbers above? In the nickel problem you multiplied the “number of” by the “value of” and thus 5 *.05 =.25 = 25 cents In the dime problem you divided the value of the money by the value of one dime dimes

5. R Read the problem over and over until you feel you understand the problem. 1. The Hurrah Players sold 600 tickets to a recent event. Adults paid $5 each and students paid $2 each. If the total collected was $2025, how many tickets of each type were sold? You might make a casual guess. 250 adult and 350 student tickets for example How could you check your guess? By multiplying the “how many” number by the “value of” number. 250 * $5 + 350 * $2 = $1950 Since the total is not $2025 we know this guess isn’t right.

6. I’m ready to get this problem done so algebra is going to be a lot quicker than guessing. Let’s chart the information as follows: How manyValue ofTotal Adult Student Tickets 5 2 Total6002025 This is the information I have!

7. Now let’s add the algebra. Since the number of adult tickets is unknown, let # of adult tickets = x How manyValue ofTotal Adult Student Tickets 5 2 Total6002025 x How would we represent the number of student tickets? If you said x, that would make x = 300 automatically since x also represents adult tickets. Not right.

8. How manyValue ofTotal Adult Student Tickets 5 2 Total6002025 x How would we represent the number of student tickets? When you know a total (600) and x represents part of that total, use subtraction total - part 600-x = number of student tickets. 600 - x

9. How manyValue ofTotal Adult Student Tickets 5 2 Total6002025 x Now we must multiply “how many” by “value of” and put in total column. 600 - x 5x 2(600 - x)

10. Form the equation. The money from the student tickets and the money from the adult tickets should add up to equal the total amount collected. cost adult tickets + cost student tickets = total collected 5x + 2(600 – x) = 2025 5x + 1200 - 2x = 2025 3x + 1200 = 2025 3x = 825 x = 275 adult tickets 600 - 275 = 325 student tickets

11. Its your turn to practice money problems.

12. 1. Yolanda has dimes and quarters totaling $5.25. If she has 33 coins in all how many of each does she have? 2. Tony has 39 bills in fives and tens. If the total value is $285 how many of each does he have? 3. The Drama Club sold 500 tickets to their fall performance. The adult tickets were $5 each and the student tickets were $3 each. If they took in $2080, how many of each did they sell? 4. Edie has 27 coins in dimes and quarters. If the total value is $3.75 how many of each does she have? Directions: work out problems 1-6 then check the solutions found on next slide.

13. 5. Venus bought 40 stamps for $12.40. Some of the stamps were 33-cent stamps and some were 23 cent stamps. How many of each did she buy? 6. Sonia has 26 bills in ones and fives. If their total value is $50 how many of each does she have?

14. Answers to Practice Problems 1.20 dimes and 13 quarters 2.21 fives and 18 tens 3.290 adult tickets and 210 student tickets 4.20 dimes and 7 quarters 5.32 stamps at 33cents each and 8 stamps at 23 cents each 6.20 $1 bills and 6 $5 bills Complete Solutions Follow

15. 1. Yolanda has dimes and quarters totaling $5.25. If she has 33 coins in all how many of each does she have? Number Of Coins Value of Coins Total Multiply previous two columns Dimesx.10.10x quarters33-x.25.25(33-x) Total 33 coins $5.25 The equation is the sum of the last column =‘s total or.10x +.25(33-x)= 5.25.10x +8.25 -.25x=5.25 -.15x=-3 x = 20 dimes 33-x = 13 quarters

16. 2. Tony has 39 bills in fives and tens. If the total value is $285 how many of each does he have? Number Of Bills Value of Bills Total Multiply previous two columns Fivesx55x Tens39-x1010(39-x) Total 39 bills $285 The equation is the sum of the last column =‘s total or 5x + 10(39 – x)= 285 5x + 390 –10x =285 -5x = -105 x = 21 fives 39-x = 18 tens

17. 3. The Drama Club sold 500 tickets to their fall performance. The adult tickets were $5 each and the student tickets were $3 each. If they took in $2080, how many of each did they sell? Number Of Tickets Cost of a Ticket Total Multiply previous two columns Adultx55x Student500-x33(500-x) Total 500 tickets $2080 The equation is the sum of the last column =‘s total or 5x + 3(500 – x)= 2080 5x + 1500 –3x =2080 2x = 580 x = 290 adult tickets 500-x = 210 student tickets

18. 4. Edie has 27 coins in dimes and quarters. If the total value is $3.75 how many of each does she have? Number Of Tickets Cost of a Ticket Total Multiply previous two columns Dimesx.10.10x Quarters27-x.25.25(27-x) Total 27 coins $3.75 The equation is the sum of the last column =‘s total or.10x +.25(27 – x) = 3.75.10x +6.75 -.25x =3.75 -.15x = -3 x = 20 dimes 27-x = 7 quarters

19. 5. Venus bought 40 stamps for $12.40. Some of the stamps were 33-cent stamps and some were 23 cent stamps. How many of each did she buy? Number Of Tickets Cost of a Ticket Total Multiply previous two columns 33 cent stamps x.33.33x 23 cent40-x.23.23(40-x) Total 40 stamps $12.40 The equation is the sum of the last column =‘s total or.33x +.23(40-x)=12.40.33x +9.2 -.23x=12.40.10x = 3.20 x = 32 33 cent stamps 40-x = 8 23 cent stamps

20. 6. Sonia has 26 bills in ones and fives. If their total value is $50 how many of each does she have? Number Of Tickets Cost of a Ticket Total Multiply previous two columns onesx1x fives26-x55(26-x) Total 26 bills $50 The equation is the sum of the last column =‘s total or x + 5(26 – x)=50 X + 130 –5x = 50 -4x = -80 X = 20 ones 26 – x = 6 fives

21. Now its time to go to the Mixture ProblemsMixture Problems