Question

To begin, have each person in the group try this puzzle: Take your seven-digit phone number and enter the first three digits on your calculator. Multiply this number by 80. Add 1 to the product. Multiply this sum by 250. Add the last four digits of your phone number to this result. Add the last four digits of your phone number again. Divide this value by 2. Subtract 125 from this number. The result should be your seven-digit phone number. Are you surprised?
In this activity we investigate the mathematics behind the puzzle. We begin by letting each digit of your phone number be represented by a different variable:
Phone number: abc-defg
1. Write down the variable expression representing the first three digits.
2. Write down an expression representing this number multiplied by 80.
3. Add 1 to the expression from step 2 and write the result.
4. Now take the expression from step 3 and multiply the entire sum by 250. Make sure you include parentheses where necessary.
5. Write the variable expression representing the last four digits of your phone number.
6. Add the last four digits of the phone number to the expression from step 4.

7. Add the last four digits again.
8. At this point, take time to simplify your expression. You may need to use the distributive property and collect like terms.
9. Now take the simplified algebraic expression from step 8 and divide the entire mathematical statement by 2.
10. Subtract 125 from your answer in step 9.
11. The result should be your seven-digit phone number. Discuss in your group how the algebraic expression in Discuss in your group how the algebraic expression in step 10 properly places the digits in their respective positions to form a phone number.

Answer 1

let first 3 digits are abc

step 2

multiplying by 80

80 abc

step 3

adding 1 to the expression

80 abc + 1

step 4

multiplying entire sum by 250

250 ( 80 abc + 1 )

= 20000 abc+ 250

step 5

last 4 digits of the number are

defg

step 6

adding it to step 4

20000 abc + 250 + defg

step 7

adding the last 4 digits again

20000 abc + 250 + defg + defg

step 8

20000 abc + 250 + 2 defg

step 9

dividing entire expression by 2

10000 abc + 125 + defg

step 10

subtract 125 from the expression

10000 abc + defg

our number was

abcdefg