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### Richard Briston's Math Assignments

## Number Tricks Assignment: Student Solutions

Question 1
choose a number = x
add 3 = x+3
multiply by 2 = 2(x+3)
add 4 = 2x+10
divide by 2 = x+5
subtract the number you started with
the result is = 5
Question 2
choose a number = x
double it = 2x
add 9 = 2x+9
add the number you started with
= 3x+ 9
divide by 3 = x+3
add 4 = x+7
subtract the number you started with
the result is = 7
Question 3
choose a number = x
add 5 = x+5
multiply by 4 = 4x+20
add 8 = 4x+28
divide by 4 = x+7
subtract the number you started with (x)
the result is = 7

### From Jenna Stevenson:

Q.1.
choose a number x
add a 3 x+3
multiply by 2 2(x+3) or 2x+6
add 4 2x+10
divide by 2 x+5
subtract # started with 5
Q.2.
choose a number x
double it 2x
add 9 2x+9
add # started with 3x+9
divide by 3 x+3
add 4 x+7
subtract # started with 7
Q.3.
choose a number x
double it 2x
add 3 2x+3
add # started with 3x+3
divide by 3 x+1
subtract # started with 1

### From Brie Pilley:

Question 1
Choose A Number x
Add 3 x+3
Double The Result 2x+6
Add 4 2x+10
Divide By 2 x+5
Subtract Original Number =5
Question 2
Choose A Number x
Double The Number 2x
Add 9 2x+9
Add Original Number 3x+9
Divide By 3 x+3
Add 4 x+7
Subtact Original Number =7
Question 3
Choose A Number x
Add 2 x+2
Double The Result 2x+4
Divide By 2 x+4
Subtract Original Number =4

### From Jackie Welch:

Question 1 Resulting number: 5
Algebraic proof :
Choose a number: x
Add 3: x+3
Multiply by 2 2(x+3) or 2x+6
Add 4 2x+10
Divide by 2 x+5
Subtract starting #: 5
Question 2 Resulting number: 7
Algebraic proof:
Choose a number: x
Double it 2x
Add 9 2x+9
Add starting #: 3x+9
Divide by 3: x+3
Add 4 x+7
Subtract starting #: 7
Question 3 My Own Trick
Choose a number.
Multiply by 2.
Subtract 3.
Add 5.
Divide by 2.
Subtract the number you started with.
Result: 1
Algebraic proof :
Choose a number: x
Multiply by 2: 2x
Subtract 3 2x-3
Add 5 2x+2
Divide by 2 x+1
Subtract starting #: 1
Question 4 - Bonus Result: 7
Algebraic Proof:
r is the remainder of matches
a is the first digit
b is the second digit
f is the final match count
1) r= 10a+b because a is the tens digit and b is the ones digit
2) f ! = (20 - x) - (a + b) - 2
f = r - (a+b) - 2
f = 10a + b - (a + b) - 2
f = 9a - 2 because r can only = 11-19 ,
a = 1
f = 7

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Richard Briston

28 January 1996