Question

14 The people working for a company work in Team A or in Team B. number of people in Team A: number of people in Team B = 3/4; 4/5 of Team A work full time. 24% of Team B work full time. Work out what fraction of the people working for the company work full time. Give your fraction in its simplest form.

Answer 1

Let's denote the number of people in Team A as a, and the number of people in Team B as b. From the problem, we know that:

a/b = 3/4

Now, we also know that 4/5 of Team A and 24% (or 24/100 = 6/25) of Team B work full time. So, the number of people working full time from Team A is 4a/5 and from Team B is 6b/25.

The total number of people working for the company is a + b, and the total number of people working full time is 4a/5 + 6b/25.

We are asked to find the fraction of people working full time, which can be represented as:

(4a/5 + 6b/25) / (a + b)

Firstly, we need to have a common denominator for the fractions, so we can express 4a/5 as 20a/25:

`(20a/25 + 6b/25) / (a + b)`

Simplifying, we can write this as:

`(20a + 6b) / (25(a + b))`

Now, since we know a/b = 3/4, we can substitute a = 3b/4 in the above expression:

`(20*(3b/4) + 6b) / (25((3b/4) + b))`

Simplifying the above, we get:

`(15b + 6b) / (25((3b/4) + b)) = 21b / 25b`

So, the fraction of people working full time is 21/25.