I have no idea what the answer is to this question
Well, we could try adding up odd numbers, and look to see when we reach 400. But I'm hoping to find an easier way.
First of all ... I'm not sure this will help, but let's stop and notice it anyway ...
An odd number of odd numbers (like 1, 3, 5) add up to an odd number, but
an even number of odd numbers (like 1,3,5,7) add up to an even number.
So if the sum is going to be exactly 400, then there will have to be an even
number of items in the set.
Now, let's put down an even number of odd numbers to work with,and see
what we can notice about them:
1, 3, 5, 7, 9, 11, 13, 15 .
Number of items in the set . . . 8
Sum of all the items in the set . . . 64
Hmmm. That's interesting. 64 happens to be the square of 8 .
Do you think that might be all there is to it ?
Let's check it out:
Even-numbered lists of odd numbers:
1, 3 Items = 2, Sum = 4
1, 3, 5, 7 Items = 4, Sum = 16
1, 3, 5, 7, 9, 11 Items = 6, Sum = 36
1, 3, 5, 7, 9, 11, 13, 15 . . Items = 8, Sum = 64 .
Amazing ! The sum is always the square of the number of items in the set !
For a sum of 400 ... which just happens to be the square of 20,
we just need the <em><u>first 20 consecutive odd numbers</u></em>.
I slogged through it on my calculator, and it's true.
I never knew this before. It seems to be something valuable
to keep in my tool-box (and cherish always).
43 times 68.
43
x68
8 times 3 is 24. Bring the 2 over the 4.
8 times 4 is 32. Add 4. Equals 36.
Answer so far is 364.
Add a 0 before answering.
3 times 6 is 18. Bring the 1 over the 4.
4 times 6 is 24. Add 4. Equals 28.
Answer so far is 288
Add 364 + 288
Final answer is 652.
Z = 3 (This equation is a given)
z(y) = 12 ( This equation is also given)
3y = 12 (as z = 3, plug 3 into z)
3y/3 = 12/3 (isolate the y by dividing 3 to both sides)
* you divide 3 to both sides because of the equal sign. What you do to one side you do to the other
y = 4 (answer for y)
y + 5 (what you are solving for)
(4) + 5 = 9 (As y = 4, plug in 4 for y in this equation)
y + 5 = 9 (4 + 5 = 9, or addition property)
9 is your answer
hope this helps
