Video: AQA GCSE Mathematics Foundation Tier Pack 3 • Paper 2 • Question 22

A ship has a crew of 140 men and 110 women. Unfortunately, some of the ship’s crew has contracted the flu and are unable to perform their duties. 35% of the men are sick and 10% of the women are sick. In order to sail, the ship needs at least 74% of its crew to perform their duties. Can the ship sail? You must show your working.

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Video Transcript

A ship has a crew of 140 men and 110 women. Unfortunately, some of the ship’s crew has contracted the flu and are unable to perform their duties. 35 percent of the men are sick and 10 percent of the women are sick. In order to sail, the ship needs at least 74 percent of its crew to perform their duties. Can the ship sail? You must show your working.

The question is, can the ship sail? To sail the ship, we need 74 percent of the crew that are well enough to perform their duties. We need to know how many people this 74 percent would represent. The total crew represents the number of men plus the number of women, 140 plus 110. The total crew is 250 people.

We know that 74 percent is 74 out of 100. And we multiply that 74 over 100 times 250. We could also write 74 percent as 0.74 and then multiply 0.74 times 250. When we do that multiplication, we get 185. The ship needs at least 185 crew members in order to sail.

Now we need to consider how many men and how many women are well enough to perform their duties. If 35 percent of the men have the flu, that means 65 percent of the men are well. We know this because 35 plus 65 equals 100. If we take the 65 percent of the men that are well and write it as a decimal, 0.65, we multiply that by the number of men in the crew, 140, and we find out that 91 of the men are well.

We’ll follow the same procedure for the women. If 10 percent of the women have the flu, then 90 percent of the women are well. We write 90 percent as a decimal 0.90, which we’re going to multiply by 110, which is the total number of women, 0.90 times 110. So there are 99 women that do not have the flu.

Using this information, the crew that can work is the 91 well men and the 99 well women. For a total of 190 crew members, 190 is greater than 185. Remember, this 185 is the required 74 percent. We have more than that. We have 190 crew members that can work. So we say yes, the ship can sail.

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