Ok so in class this is what our teacher had us do....
1.Pick a number to represent the number of times you would like to have chocolate in a week (more than once, but less than 10 times).
2.Double this amount (just to be bold).
3.Add 5.
4.Multiply the result by 50.
5.If you have already had your birthday this year, add 1766. If you haven’t yet had your birthday, add 1765.
6.Now, subtract the four digit year you were born.
7. Your result is a three digit number. The first digit is the number of times you chose to have chocolate in a week and the next two
After that she gave us an assignment. The homework assignment is to...
1. Develop an algebraic expression to model the steps we went through
2.Justify why this “worked” the way it did.Basically why does the number you pick have to be greater than 1 and less than 10?
1. To develop an algebraic expression for the steps given in class, let's break down each step and define variables:
Step 1: Pick a number to represent the number of times you would like to have chocolate in a week. Let's call this number "n".
Step 2: Double this amount. So the new value is 2n.
Step 3: Add 5 to the doubled amount. The new value is 2n + 5.
Step 4: Multiply the result by 50. The new value is 50(2n + 5).
Step 5: If you have already had your birthday this year, add 1766. If not, add 1765.
Let's call the final value after step 5 as "x". Therefore, the expression becomes:
x = 50(2n + 5) + 1766 (if birthday has passed)
or
x = 50(2n + 5) + 1765 (if birthday has not passed)
2. Now, let's justify why the number you pick has to be greater than 1 and less than 10.
In this sequence of steps, the number you pick represents the number of times you would like to have chocolate in a week. It is important to note that steps 4, 5, and 6 rely on the number of times you chose to have chocolate in a week being a three-digit number.
Step 4 requires multiplication to give a value that is four digits or more since we are multiplying by 50. Therefore, the original number of times you chose to have chocolate in a week should be two digits or less.
Step 5 adds either 1766 or 1765 to the result obtained in step 4. Since we need the final value (x) to be a three-digit number, the added values (1766 or 1765) need to be greater than 1000. This means the original number of times you chose to have chocolate in a week should be one digit only.
Therefore, the number you pick has to be greater than 1 and less than 10, ensuring that the final result in step 7 is a three-digit number.
To develop an algebraic expression to model the steps you went through, let's break down each step:
1. Pick a number to represent the number of times you would like to have chocolate in a week (more than once, but less than 10 times).
Let's call this number "x".
2. Double this amount (just to be bold).
Multiply the number "x" by 2, which gives us 2x.
3. Add 5.
Add 5 to 2x, which gives us 2x + 5.
4. Multiply the result by 50.
Multiply 2x + 5 by 50, giving us 50(2x + 5).
5. If you have already had your birthday this year, add 1766. If you haven’t yet had your birthday, add 1765.
Let's assume we have already had our birthday, so we add 1766 to 50(2x + 5), resulting in 50(2x + 5) + 1766.
6. Now, subtract the four-digit year you were born.
Let's call the four-digit year you were born "y". So, subtracting y from 50(2x + 5) + 1766 gives us 50(2x + 5) + 1766 - y.
7. The result is a three-digit number. The first digit is the number of times you chose to have chocolate in a week, and the next two digits represent the year you were born.
Therefore, the algebraic expression to model the steps can be written as:
50(2x + 5) + 1766 - y
Now, let's discuss why the number you pick has to be greater than 1 and less than 10.
In the given steps, we first double the number chosen, add 5, and then perform various mathematical operations. If the number chosen is 1 or less, then doubling it would result in a number less than or equal to 2. This would make the subsequent arithmetic operations insignificant, as adding 5, multiplying by 50, and performing additional additions would not significantly change the outcome.
Similarly, if the chosen number is 10 or more, then doubling it would result in a number greater than or equal to 20. Again, the subsequent calculations would not strongly influence the final result.
Therefore, choosing a number greater than 1 and less than 10 ensures that the resulting expressions in the algebraic expression are significant and meaningfully affect the final outcome.