1. IZZY ÉVEUX’S P U B L I S H E D N O T E S

2. A few families took a trip to an amusement park together. Tickets cost $6 for adults and $3.50 for kids, and the group paid $36.50 in total. There were 5 fewer adults than kids in the group. Find the number of adults and kids on the trip.

3. First, let’s set some equations up... If each adult costs $6. let “x” represent the number of adults, and 6 represent the cost of each adult your value for any number of adults is : 6x

4. Next... If each kid costs $3.50. let “y” represent the number of kids, and 6 represent the cost of each kid your value for any number of kid is: 3.5y

5. We know that the total cost for the group is $36.50... Therefore: The cost of adults plus the cost of kids, equals $36.50 6x + 3.5y = $36.50 OR… Being the price per any number of adults Being the price per any number of children

6. Based on the information given... There are 5 fewer adults than there are children. Meaning, for example, if there are 10 children (y), there are 5 fewer adults (x) than 10 children (y), or 5 adults (x). X = y-5 AN EQUATION TO REPRESENT THIS STATEMENT IS:

7. How many adults and kids are there, really? Our first equation that we found: 6x + 3.5y = $36.50 X = y-5 And our second equation that we found: Can be used to find how many adults and kids there are using both elimination and substitution...

8. Now we know that y = 7, we can substitute 7 for y in the equation: X = y-5 to find x... X = y-5 X = 7-5 X = 2 That means that there are 2 ADULTS (represented by X) and 7 CHILDREN (represented by Y).

9. NEXT QUESTION…

10. THE SUM OF TWO NUMBERS Is 35, and the difference is 1. what are these two numbers?

11. First, let’s set some equations up... Let the two numbers be represented by x and y The sum of these two numbers is 35. x + y = 35

12. Next... The difference of these two numbers is 1 X - y = 1

13. If... X - y = 1 x + y = 35 Then we can use elimination for solve for X and y

14. Let’s add these two equations: + (X -y = 1) (x + y = 35) 2x = 36 x = 18 SOLVING FOR X

15. If... X = 18 Then we can solve for y using either of our original equations. Let’s use: (x + y = 35). Substituting X for 18... (18) + y = 35 y = 35 -18 y = 17 X = 18 Y on one side of the equation Solve for Y

16. x = 18 y = 17

17. To graph the two original equations... X - y = 1 x + y = 35 Put the two equations in slope-intercept format. Y = -x + 35 Y = x - 1

19. LET’S C R E A T E A P R O B L E M !

20. START BY PICKING TWO RANDOM NUMBERS: 45 AND 16

21. THE SUM OF 45 AND 16 IS 61 I’m sixty- one

22. THE DIFFERENCE OF 45 AND 16 IS 29 I’m twenty- nine

23. NOW THAT WE HAVE OUR TWO STATEMENTS, WE CAN FINISH THE QUESTION... THE SUM of two numbers is 61. THE DIFFERENCE BETWEEN THESE TWO NUMBERS Is 29. WHAT ARE THESE TWO NUMBERS?

24. LET’s solve it like we did with a previous problem... THE SUM OF TWO NUMBERS Is 61, and the difference is 29. what are these two numbers?

25. First, let’s set some equations up... Let the two numbers be represented by x and y The sum of these two numbers is 61. x + y = 61

26. Next... The difference of these two numbers is 29 X - y = 29

27. If... X - y = 29 x + y = 61 Then we can use elimination for solve for X and y

28. Let’s add these two equations: + (X -y = 29) (x + y = 61) 2x = 90 x = 45 SOLVING FOR X

29. If... X = 45 Then we can solve for y using either of our original equations. Let’s use: (x + y = 61). Substituting X for 45... (45) + y = 61 y = 61 -45 y = 16 X = 45 Y on one side of the equation Solve for Y

30. x = 45 y = 16

31. THE END.