2021 PSLE Maths coin question: Simplest solution
Have you ever been given a complex Maths problem that seemed daunting at first, but then turned out to be quite simple? That's exactly what we're going to explore in this blog. We'll be looking at a seemingly complex Maths problem that involves calculating the mass of coins, but with a little bit of logic and some basic Maths skills, it becomes a breeze.
Specifically, we'll be answering the Helen and Ivan Coin question that stumped many students during the 2021 Maths exam.
Let's look at the question first:
Helen and Ivan had the same number of coins. Helen had a number of 50-cent coins and 64 20-cent coins.
These coins had a mass of 1.134 kg.
Ivan had a number of 50-cent coins and 104 20-cent coins.
Question 1: Who has more money in coins and by how much?
Question 2: Given that each 20-cent coin is 2.7 g heavier than 50 cent coin, what’s the mass of Ivan’s coins in KG?
In order to answer this, let’s try to draw this problem, so we can understand what's being asked.
Let’s look at the question again.
If you notice closely, the first line of the question mentions that Helen and Ivan have the same number of coins.
Keep this in mind.
Now, for the first question, we want to know who has more money and by how much.
Since we know the number of 20-cent coins both Helen and Ivan have, we can start solving our question using these numbers.
Helen: 64
Ivan: 104
Let’s calculate the difference.
We can see that Ivan has 40 more 20-cent coins than Helen (104-64)
Since the number of coins for both is the same, we can conclude that Helen has 40 50-cent coins more than Ivan.
That’s all the information that we have.
Now, we know that there’s a difference of 40 coins.
Ivan has 40 20-cent coins more than Helen (40*20 cents = 800 cents), and Helen has 40 50-cent coins more than Ivan (40*50 cents = 2000 cents).
So, clearly, Helen has 1200 cents (or $12) more than Ivan.
That’s our answer.
Let’s look at the next question, this time we need to look at the mass of the coins.
Except for those 40 extra coins, the mass of coins that Helen and Ivan have is the same.
Since 50-cent coins are 2.7 grams heavier than 20-cent coins, we can say that Helen’s coins weighed 40 x 2.7 g = 108 g heavier than Ivans’.
Given that the total mass of Helen’s coins is 1.134 kg or 1134 g, the mass of Ivan’s coins would be 1124 - 108 = 1016 g or 1.026 kg.
Doesn’t it all make sense when it’s explained?
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