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Question

Hihi,

Can any experts help on how to solve the below check & guess P5 questions?

1. Shawn waited at the bus stop for 15 mins and saw 39 vehicles go past. He counted a total of 124 wheels and notice that only cars and motorcycles went past. How many cars went past Shawn?

2. Ryan had 44 more 20 cent coins than 50 cents coin. The total value of the 50 cents coins is $2 more than the total value of 20 cents coin.
A) how many 50 cents coins are there in his coin box?
B) how much does Ryan have?

Answer

1. Shawn waited at the bus stop for 15 mins and saw 39 vehicles go past. He counted a total of 124 wheels and notice that only cars and motorcycles went past. How many cars went past Shawn?

1. Note that cars have 4 wheels and motorcycles have 2 wheels.
SUPPOSE all 39 vehicles were motorcycles. We should see
only 39 x 2 = 78 wheels. But we saw 124, which is an extra
124 - 78 = 46 wheels. The extra wheels came from the cars,
each contributing 4 - 2 = 2 more wheels to the count.
So there are 46/2 = 23 cars.

2. SUPPOSE Ryan gave away 44 of his 20 cent coins, which is $8.80.
That means
- he now have the same number of 20 cent and 50 cent coins
- the total value of the 50 cents coin is now $10.80 more than
  the total value of the 20 cents coin.
Since each 50 cent coin is worth 30 cents more than a 20 cent coin,
that means (a.) there are 1080/30 = 36 of the 50 cents coin.

(b.) Number of 20 cent coins is 36 + 44 = 80.
So Ryan has total of 80 x 0.20 + 36 x 0.50 = 16 + 18 = $34

 

I think these are “supposition” questions, rather than “guess and check”. There is no guessing at all. Both of these questions have 2 varying quantities. We “suppose” some scenario to make one of the 2 quantities the same and then solve it from there.

In Q1, we have number of cars-vs-motorcycles and 2-wheels-vs-4-wheels. So we suppose they are all motorcycles to make them 2-wheels. The excess wheels must then come from cars. We could have also supposed there were all cars. Then we would have a shortage of wheels due to some of the vehicles actually being motorcycles.

In Q2, we have number of 20c-vs-50c coins and different values of coins. So we suppose Ryan gave aways 44 of the 20c to make the number of coins the same. We could have suppose Ryan was given 44 more 50c coins and came to the same conclusion.

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