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Flores, John Rey A.
Lopez, Atasha Isabel R.
Villanueva, Hubertcel S.
MPSMIM - Problem Solving, Mathematical Investigation and Modelling
Learning Task 2
1. Andy’s lawn has twice as much area as Beth’s lawn and three times as much area as
Carlos’ lawn. Carlos’ lawn mower cuts half as fast as Beth’s mower and one third as fast
as Andy’s mower. They all start to mow their lawns at the same time. Who will finish
first?
Flores, John Rey A.
Lopez, Atasha Isabel R.
Villanueva, Hubertcel S.
2. Solve 12 𝑥
4
3
2
Flores, John Rey A.
Lopez, Atasha Isabel R.
Villanueva, Hubertcel S.
- If 𝑎, 𝑏 satisfy
𝑎 + 𝑏 = 3 and 𝑎
2
2
Then, what is 𝑎
3
3
- The first thing we need to do is to raise both sides to 3 we have (𝑎 + 𝑏)
3
3
which (𝑎 + 𝑏)
3
Now, note that:
3
3
3
then we have
3
3
3
3
since 𝑎 + 𝑏 = 3 , substitute 3 to the equation we have
3
3
to find 𝑎𝑏, we will use 𝑎
2
2
= 5 and 𝑎 + 𝑏 = 3
2
2
2
2
2
2
2
2
2
2
by substitution in the last equation,
3
3
3
3
3
3
3
3
Thus,
3
3
Flores, John Rey A.
Lopez, Atasha Isabel R.
Villanueva, Hubertcel S.
- Let 𝑎, 𝑏, 𝑐 ∈ ℝ, 𝑠. 𝑡.
If 𝑎𝑏𝑐 = 13 , what is 𝑎 + 𝑏 + 𝑐?
next we substitute 𝑎𝑏𝑐 = 13 ; 𝑎𝑏 =
13
𝑐
13
𝑏
13
𝑎
now we let 𝑎 + 𝑏 + 𝑐 = 𝑥
since, 𝑎 + 𝑏 + 𝑐 = 𝑥, therefore 𝑎 + 𝑏 + 𝑐 = − 13
