Math Olympiad Strategies Money Wise Ashley gave Ben and Chris as much money as each had Then Ben gave Ashley and Chris as much money as each already had Then Chris gave Ashley and Ben as much money as each had Then each of the three people had 24 How much money did each have to begin wit ID: 380947
Download Presentation The PPT/PDF document "Working Backwards" is the property of its rightful owner. Permission is granted to download and print the materials on this web site for personal, non-commercial use only, and to display it on your personal computer provided you do not modify the materials and that you retain all copyright notices contained in the materials. By downloading content from our website, you accept the terms of this agreement.
Slide1
Working Backwards
Math Olympiad StrategiesSlide2
Money Wise
Ashley gave Ben and Chris as much money as each had. Then Ben gave Ashley and Chris as much money as each already had. Then Chris gave Ashley and Ben as much money as each had. Then each of the three people had $24. How much money did each have to begin with?
This problem has 4 stages. The only amount that is known is in the fourth stage, which is the final outcome. Let’s consider the stages in reverse order and make a table:
STAGE
ACTION
Ashley
Ben
Chris
SUM
4
Each
ends with $24
$24
$24
$24
$72
3
Chris gave
Ashley and Ben half of what each will have in stage 4
$12
$12
$48
$72
2
Ben gave Ashley and Chris half of what each will have in stage 3.
$6
$42
$24
$72
1
Ashley gave Ben and Chris half of what each will have in stage 2.
$39
$21
$12
$72Slide3
Inverse Flow
What number belongs in the START circle of this “flow chart”?
To find the starting number use the inverse of each operation in reverse order:
32 divided by 8 plus 5 multiply by 2 = ?
The number in the START circle is 18.Slide4
Work Backwards Strategy
Homework NAME:______________________________Due:____________________________
I went into a store and spent half of my money and then $20 more. I went into a second store and spent half of my remaining money and then $20 more. Then I had no money left. How much money did I have when I went into the first store?
What number belongs in the
START
box of this “flow chart”
?
At the end of one school day a teacher had 17 crayons left. The teacher remembered giving out 14 of all her crayons in the morning, getting 12 crayons back at recess, and giving out 11 crayons after lunch. How many crayons did the teacher have at the start of the day
?
I have a Magic Money Box that will double any amount of money placed in it and then add $5 to the doubled amount. Today I placed a certain amount of money in the box. The box then gave me a new amount, which I placed back into the box. This time the box gave me $43. How much money did I first place in the Magic Money Box?
A cooperative farm has three subdivisions, A, B, and C; the subdivisions lend equipment to each other as needed.
In the beginning A lent B and C as many reapers as each then had. Several months later B lent A and C as many reapers as each had then. The following spring C lent A and B as many repers as each then had. Each subdivision then had 16 reapers. How many reapers did each have to begin with?