Where did that add 40 subtract 40 come from in the end?
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Module 2 Week 3 Day 10 Your Turn Explanation Part 2
Where did that add 40 subtract 40 come from in the end (around 8:15?)
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Hi TSS Graviser,
That's a great question! What Prof. Loh did here is he came up with a pair of numbers that would satisfy both equations he wrote: \( \frac{a+b}{2} = 180 \) and \( a-b = 80 \). The equation \( \frac{a+b}{2} = 180 \) represents the average, or the midpoint, between \( a \) and \( b \). Since the difference between the two numbers is 80, \( a \) and \( b \) should each be 40 degrees away from the average. And because \( a \) is greater than \( b \), 40 should be added to 180 (the average) for \( a \) and subtracted from 180 for \( b \). This gives us
\( a = 180+40 = 220 \) and \( b = 180-40 = 140 \).
Please let us know if you are still confused!
Happy Learning,
The Daily Challenge Team -
why not 36 plus 44?
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Hi again!
36 and 44 do add up to 80, which fulfills one of the equations given: \( a-b = 80 \). Now, let's see if it satisfies the other equation, \( \frac{a+b}{2} = 180\). There are two possible cases:
- \( a = 180+36 = 216 \) and \( b = 180-44 = 136 \)
- \( a = 180+44 = 224 \) and \( b = 180-36 = 144 \)
(We are only adding numbers to \( a \) because it must be greater than \( b \).)
For the first case, the average (\( \frac{a+b}{2} \)) would be:
\( \frac{216+136}{2} = \frac{352}{2} = 176 \)For the second case, the average would be:
\( \frac{224+144}{2} = \frac{368}{2} = 184 \)Hence, when we use 36 and 44, it does not satisfy \( \frac{a+b}{2} = 180\). In fact, this is true for all pairs of numbers other than 36 and 44. I hope this helps!
Happy Learning,
The Daily Challenge Team
