Use algebra pieces and mental arithmetic to determine four consecutive odd numbers who sum is 64. Sketch and label your algebra piece model and explain how you solved the problem.
I'd start by dividing 64 by 4.
that would give me 16 but that's not an odd number
You're right.
What are the four odd numbers closest to 16?
Do they add up to 64?
yes 13,15,17,19 thanks :)
You're welcome. :-)
To solve this problem using algebra pieces and mental arithmetic, we can follow these steps:
Step 1: Let's represent the first odd number as "x".
Step 2: Since we know that the numbers are consecutive odd numbers, we can represent the other three numbers as "x + 2", "x + 4", and "x + 6". Here, we add 2 to get the next odd number, and continue adding 2 to get the subsequent odd numbers.
Step 3: We can now write an equation to represent the sum of these numbers: x + (x + 2) + (x + 4) + (x + 6) = 64.
Step 4: Simplify the equation: 4x + 12 = 64.
Step 5: Subtract 12 from both sides to isolate the variable: 4x = 52.
Step 6: Divide both sides by 4 to solve for "x": x = 13.
Now we have the value of the first odd number, which is 13. We can use this to find the other three consecutive odd numbers.
First odd number = x = 13
Second odd number = x + 2 = 13 + 2 = 15
Third odd number = x + 4 = 13 + 4 = 17
Fourth odd number = x + 6 = 13 + 6 = 19
Therefore, the four consecutive odd numbers with a sum of 64 are 13, 15, 17, and 19.