## Number Tricks Assignment: Student Solutions

### From Jori VanGorder:

```Question 1

choose a number = x
multiply by 2   =  2(x+3)
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 the number you started with
= 3x+ 9
divide by 3     = x+3
subtract the number you started with
the result is   = 7

Question 3

choose a number = x
multiply by 4   = 4x+20
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
multiply by 2             2(x+3) or 2x+6
divide by 2               x+5
subtract # started with   5

Q.2.

choose a number           x
double it                 2x
divide by 3               x+3
subtract # started with   7

Q.3.

choose a number           x
double it                 2x
divide by 3               x+1
subtract # started with   1
```

### From Brie Pilley:

```Question 1

Choose A Number           x
Double The Result         2x+6
Divide By 2               x+5
Subtract Original Number  =5

Question 2

Choose A Number           x
Double The Number         2x
Divide By 3               x+3
Subtact Original Number   =7

Question 3

Choose A Number           x
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
Multiply by 2             2(x+3) or 2x+6
Divide by 2               x+5
Subtract starting #:      5

Question 2 Resulting number: 7
Algebraic proof:
Choose a number:          x
Double it                 2x
Divide by 3:              x+3
Subtract starting #:      7

Question 3 My Own Trick

Choose a number.
Multiply by 2.
Subtract 3.
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
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
```