Freya has red and blue poker chips. The red chips are worth 20 p and the blue chips are worth 50 p. She has twice as many blue chips as red chips. The total value of her chips is 14 pounds 40. Work out the number of blue chips that Freya has.
Well, for this question, I’m gonna call the red chips 𝑟 and the blue chips 𝑏. So therefore, what we can do is set up a couple of equations. The first equation we can set up is that 𝑏 is equal to two 𝑟. And that’s because we’re told the Freya has twice as many blue chips as she does red chips. So the number of blue chips is equal to two multiplied by the number of red chips. So we’re also told that the red chips are worth 20 p and the blue chips are worth 50 p. However, the total value of the chips is 14 pounds 40. And this is given in pounds. So what we need to do is convert our 20 p and 50 p to pounds.
So in order to convert 20 p and 50 p to pounds, what we do is we divide 20 and 50 by 100. So if we do that, we’re gonna get 20 p is equal to 0.20 pounds. Or 50 p is equal to 0.50 pounds. Okay, great. So now, we’ve got these. What we can do is create another equation.
So we’ve got a second equation now. So what we’ve got is 0.2𝑟 plus 0.5𝑏 equals 14.4. So what I’ve done is I’ve turned our money values into decimals. So I’ve removed the end zeros just to tidy up with our calculations. And then, what we’ve got is 0.2. So our 20 p multiplied by 𝑟, because 𝑟 is the number of red chips, plus our 50 p multiplied by 𝑏, which is our number of blue chips, is equal to 14.4 or 14 pounds 40. And then, what I’ve done is labeled the equations because this is gonna help us when we’re solving the problem.
So what I’m gonna do is I’m gonna substitute one into two. So I’m gonna substitute our equation one into our equation two. So that’s 𝑏 equals two 𝑟. So when I do that, I get 0.2𝑟 plus 0.5 then multiply it by two 𝑟. And that’s because we’ve substituted two 𝑟 instead of our 𝑏. And then, we get this equal to 14.4. So then, we have 0.2𝑟 plus one 𝑟. And that’s because 0.5 multiplied by two is one. Well, I’ve got one in brackets cause we don’t usually need to write the one. But I’ve put it in here just to show you that’s what we’ve got because we write one 𝑟 as just 𝑟.
So now, we can collect these like terms because we have 0.2𝑟 plus one 𝑟, which gives us 1.2𝑟. So now, we have 1.2𝑟 is equal to 14.4. So all we need to do is divide both sides of the equation by 1.2 to find out what 𝑟 is. And when we do that, we get 𝑟 is equal to 12. Now, of course, we can do this with a calculator. But if we look carefully, there’s another method we could’ve used because if we see 1.2 and 14.4 — well, when we’re dividing decimals, we can disregard the decimal because what we can say is it’s 12 and 144. Well, 144 divided by 12 is gonna be 12 because 12 squared is 144. Okay, great.
So now, we found 𝑟. But have we solved the problem? Well, no, because what we want to find out is the number of blue chips. So what I’m gonna do is I’m gonna sub 𝑟 equals 12 now into equation one to find 𝑏. So when I do that, I’m gonna get 𝑏 is equal to two multiplied by 12. So this gives us an answer of 𝑏 being equal to 24. So therefore, the number of blue chips that Freya has is 24.
So what we can do if we want is check our answer by putting the values back into our equation two. So we’d have 0.2 multiplied by 12 for the first part, which will be equal to 2.4 because that was our number of red chips multiplied by the worth of each of the red chips. And then, we’d have 0.5 multiplied by 24. And that’s because the value of the blue chips is 50 p or 0.5 pounds and multiply this by the number of blue chips, which is 24. So this gives us 12. So then, we add these together. So we’ve got 12 add 2.4, which is equal to 14.4. So this is correct because the total value of the chips is 14 pounds 40. So we’ve got that correct. And it works.
So therefore, the total number of blue chips is 24 blue chips.