One day, a group of people had a driving test - OCR - GCSE Maths - Question 19 - 2019 - Paper 2
Question 19
One day, a group of people had a driving test.
40 of this group were men and the rest were women.
$ rac{3}{5}$ of the men and $ rac{2}{3}$ of the women passed the dr... show full transcript
Worked Solution & Example Answer:One day, a group of people had a driving test - OCR - GCSE Maths - Question 19 - 2019 - Paper 2
Step 1
Identify the number of men and women.
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Answer
Given that there are 40 men, we can denote the number of women as w. The total group can be expressed as:
40+w.
Step 2
Determine the number of men who passed the test.
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Answer
According to the problem, rac{3}{5} of the men passed the driving test. Therefore, the number of men who passed is:
ext{Men passed} = rac{3}{5} imes 40 = 24.
Step 3
Determine the number of women who passed the test.
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Answer
It is stated that rac{2}{3} of the women passed the driving test. Thus, the number of women who passed is:
ext{Women passed} = rac{2}{3} imes w.
Step 4
Set up the equation for equality of passes.
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Answer
Since the number of men and women who passed the test is the same, we can set up the equation:
24 = rac{2}{3} imes w.
Step 5
Solve for the number of women.
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Answer
To find w, we first multiply both sides of the equation by 3 to eliminate the fraction:
72=2w.
Now, dividing by 2 gives:
w=36.
Thus, the number of women that took the driving test that day is 36.
