Video: AQA GCSE Mathematics Higher Tier Pack 2 • Paper 2 • Question 3

𝑦 is 150% more than 𝑥. Circle the ratio 𝑥 : 𝑦. [A] 1 : 150 [B] 2 : 3 [C] 5 : 2 [D] 2 : 5

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Video Transcript

𝑦 is 150 percent more than 𝑥. Circle the ratio 𝑥 to 𝑦. The options are one to 150, two to three, five to two, and two to five.

So first of all, in this question, let’s think what 𝑦 is 150 percent more than 𝑥 actually means. So we can write it as 𝑦 is equal to 𝑥 plus 150 percent of 𝑥, because it’s 150 percent more than 𝑥. Well, let’s break it down even further. If we think of 150 percent of 𝑥, what does this mean?

Well, “of” means multiply, so it’s 150 percent multiplied by 𝑥. Well, how else can we write 150 percent? Well, 150 percent can be written as 150 over 100. That’s because “percent” means out of 100. Well, if we divide by 100, we move each number or each digit two place values to the right. So therefore, we can say that 150 divided by 100 is gonna be equal to 1.5. So therefore, we can say that 𝑦 is equal to 𝑥 plus 1.5𝑥.

So now it’s just a case of simplifying like terms because we’ve got 𝑥 plus 1.5𝑥. Well, let’s think about what 𝑥 is. 𝑥 is just the same as one 𝑥. We just don’t write the coefficient of one. So we’ve got one 𝑥 plus 1.5𝑥. So therefore, we’ve arrived at the fact that 𝑦 is gonna be equal to 2.5𝑥.

Okay, great, but now what we need to do is turn it into a ratio 𝑥 to 𝑦. Well, the first thing we’re going to do is we’re gonna turn our equation the other way round just so it’s in the same order of 𝑥 to 𝑦. So we’ve got 2.5𝑥 is equal to 𝑦.

So then the first thing we’re gonna do is multiply each side of the equation by two. And that’s to get rid of the decimal. So we’re gonna get five 𝑥 is equal to two 𝑦. And then we’re gonna divide by five. And when we divide by five, we’re gonna get 𝑥 is equal to two over five or two-fifths 𝑦. And then, finally, divide by 𝑦. And when we divide by 𝑦, we’re gonna get 𝑥 over 𝑦 is equal to two over five or two-fifths. But how is this gonna help us? We still haven’t got it as a ratio in the form 𝑥 to 𝑦.

So to turn it into the ratio, we can use this relationship. And that is that 𝑥 over 𝑦 being equal to 𝑎 over 𝑏 tells us that 𝑥 to 𝑦 is gonna be equal to 𝑎 to 𝑏. So therefore, we can say that 𝑥 to 𝑦 is gonna be equal to two to five. And that’s because, in our scenario, the 𝑎 is the two and the 𝑏 is the five. So therefore, we can say that if 𝑦 is 150 percent more than 𝑥, then the ratio 𝑥 to 𝑦 is gonna be two to five. And I’ve circled it here as the fourth answer.

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