Question 1197952: Hi
3/4 of the boys are equal to 1/3 of the girls. What fraction of the pupils are boys. My son son 9/13 textbook solution is 4/13. Who is correct.
Thanks
Found 5 solutions by math_tutor2020, greenestamps, MathTherapy, josgarithmetic, ikleyn:
Answer by math_tutor2020(3817)   (Show Source):
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b = number of boys
g = number of girls
b+g = number of pupils
3/4 of the [number of] boys = 1/3 of the [number of] girls
(3/4)b = (1/3)g
12*(3/4)b = 12*(1/3)g
9b = 4g
9b/g = 4
b/g = 4/9
g/b = 9/4
k = fraction of the pupils that are boys
(number of boys)/(number of pupils) = k
b/(b+g) = k
(b+g)/b = 1/k
b/b + g/b = 1/k
1 + g/b = 1/k
1 + 9/4 = 1/k .... plug in g/b = 9/4
4/4 + 9/4 = 1/k
(4+9)/4 = 1/k
13/4 = 1/k
4/13 = k
k = 4/13
Answer: 4/13 of the pupils are boys.
Side note: 9/13 is the fraction of girls (since 4/13+9/13 = 1)
Answer by greenestamps(13200)  (Show Source):
You can put this solution on YOUR website!
For a preliminary analysis using logical reasoning, note that it takes nearly all of the boys to equal less than half of the girls; that means the number of girls is greater.
The other tutor showed a good algebraic solution. Here is a very different solution, using only logical reasoning and basic arithmetic.
Since 3/4 of the number of boys is equal to 1/3 the number of girls, this is one of those strange problems where we want to express those two fractions with like NUMERATORS.
1/3 = 3/9, so 3/4 of the boys is equal to 3/9 of the girls. Then, with the numerators being equal, that says that there are 4 boys for every 9 girls.
So 4/13 of the students are boys and 9/13 of them are girls.
Answer by MathTherapy(10552)  (Show Source):
Answer by josgarithmetic(39620) (Show Source):
Answer by ikleyn(52798)  (Show Source):
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