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The number of boys and girls in a class are in the ratio 7:5. The number of boys is 8 more than the number of girls. What is the total class
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The number of boys and girls in a class are in the ratio 7:5. The number of boys is 8 more than the number of girls. What is the total class strength? *
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Mathematics
4 years
2021-07-17T01:14:13+00:00
2021-07-17T01:14:13+00:00 2 Answers
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ANSWER:
The total class strength is 48 students.‼
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EXPLANATION:
Let the number of boys be 7x and that of girls be 5x.
According to the given condition, we have
Number of boys = Number of girls + 8
⇒7x = 5x + 8
⇒7x − 5x = 8 ….[Transposing 5x to LHS]
⇒2x = 8
⇒x = 8/2 = 4.
Therefore, number of boys = 7 × 4 = 28 and number of girls = 5 × 4 = 20.
So, total number of children in the class = 28 + 20 = 48.
Hence, the class strength is 48.
Answer: 48 students total
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Explanation:
If there were 7 boys and 5 girls, then we’d have the ratio of 7:5. The boys are listed first because of how your teacher mentions boys first to set up the ratio. The order is important. That means 7:5 is different from 5:7.
With 7 boys and 5 girls, we see that there are 7-5 = 2 more boys compared to girls, and not 8. The jump from 2 to 8 is “times 4”, which means we’ll need to multiply each gender count by 4 to get to the class size we want
boys: 7 —> 7*4 = 28
girls: 5 —> 5*4 = 20
Having 28 boys and 20 girls will lead to the ratio 28:20, and it reduces fully to 7:5 when we divide both parts by the GCF 4.
The total number of students is 28+20 = 48
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Here’s another way we can solve.
x = number of girls
x+8 = number of boys, since there are 8 more
The ratio of boys to girls is 7:5, meaning,
(number of boys)/(number of girls) = 7/5
(x+8)/x = 7/5
(x+8)*5 = x*7 …. cross multiply
5x+40 = 7x
40 = 7x-5x
40 = 2x
2x = 40
x = 40/2
x = 20
There are x = 20 girls and x+8 = 20+8 = 28 boys. So 20+48 = 48 total.