Video: GCSE Mathematics Foundation Tier Pack 2 • Paper 3 • Question 9

GCSE Mathematics Foundation Tier Pack 2 • Paper 3 • Question 9

02:19

Video Transcript

A bag contains blue, red, green, and yellow counters only. In total, there are 528 counters in the bag. One-third of the counters are green. 67 of the counters are red. 115 of the counters are blue. Work out how many of the counters are yellow.

So we’re told in the question that the bag only contains blue, red, green, and yellow counters. And we’re also told that the total number of counters in the bag is 528. This means that the numbers of blue, red, green, and yellow counters must sum to 528.

We’re also told in the question that 67 of the counters are red and 115 of the counters are blue. So we can substitute these values into the equation that we’ve written. We have 115 plus 67 plus the number of green counters plus the number of yellow counters is equal to 528.

The other piece of information we’re given in the question is that one-third of the counters are green. To find one-third of a number, we just divide it by three. So we divide the total number of counters, which is 528, by three, giving 176. We can perform this division on a calculator if it’s available or we can use a short division method.

Now we’ve worked out that the number of green counters in the bag is 176, so we can substitute this value into our equation. We don’t know what the number of yellow counters in the bag is, but this is what we’re looking to work out. And we now have all the information to enable us to do so. We just need to solve the equation that we’ve got.

115, 67, and 176 sum to 358. So our equation becomes 358 plus 𝑦, the number of yellow counters, is equal to 528. To solve this equation, we just need to subtract 358 from each side. And it gives 𝑦 is equal to 170. This is the number of yellow counters in the bag.

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