Video: AQA GCSE Mathematics Foundation Tier Pack 2 • Paper 2 • Question 11

A farmer takes stock of the vegetables in his field. He has 160 potatoes, 80 cabbages, and 35 turnips. Altogether, the farmer harvests 80% of the total number of vegetables. He harvests 60% of the cabbages and 28 turnips. What percentage of the potatoes did the farmer harvest?

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Video Transcript

A farmer takes stock of the vegetables in his field. He has 160 potatoes, 80 cabbages, and 35 turnips. Altogether, the farmer harvests 80 percent of the total number of vegetables. He harvests 60 percent of the cabbages and 28 turnips. What percentage of the potatoes did the farmer harvest?

Let’s start with what we know. The total number of vegetables equals the 160 potatoes plus 80 cabbages plus 35 turnips. The farmer has 275 total vegetables. He harvests 80 percent of the total number of vegetables. That would be 80 percent of 275. As a fraction, we can write 80 percent as 80 over 100, which is being multiplied by 275. You can also write 80 percent as a decimal, 0.80. Either way, you’ll need to multiply that value by 275, which gives us 220. There were 220 vegetables harvested.

We know that 60 percent of the cabbages were harvested, that is, 60 over 100, times 80 because we started with 80 cabbages. We can rewrite that fraction to be 0.60 and then multiply that by 80, which gives us 48. 48 cabbages were harvested. We also know that 28 turnips were harvested. So we take our 220 vegetables that were harvested and we subtract the 48 cabbages that were harvested and we subtract the 28 turnips that were harvested. 220 minus 48 minus 28 equals 144. This 144 represents the number of potatoes that were harvested.

We have to be careful here because our question is not asking how many potatoes were harvested, but what percentage of potatoes did the farmer harvest. To find that percentage, we take our 144 harvested potatoes and write it as a fraction over 160 total potatoes. 144 divided by 160 equals 0.90, which again is still not our percentage. To calculate the percent from this decimal, we multiply by 100. 0.90 times 100 equals 90 percent. The farmer harvested 90 percent of his potato crop.

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