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ivann1987 [24]
3 years ago
6

A grade has 81 girls and 72 boys. the grade is split into groups that have the same ratio of girls to boys as the whole grade. h

ow many girls are in a group that has 16 boys? 81:72, x:x, x:16
Mathematics
1 answer:
Arturiano [62]3 years ago
3 0

Answer:

<u>There are 18 girls in a group that has 16 boys.</u>

Step-by-step explanation:

1. Let's review the information given to us for solving the question:

Number of girls in the grade = 81

Number of the boys in the grade = 72

Number of students in the grade = 81 + 72 = 153

2. Let's find the number of girls in a group that has 16 boys.

For getting that number we will use the Rule of three simple, this way:

Number of girls in a group that has 16 boys = (81 * 16)/72

Number of girls in a group that has 16 boys = 1,296 / 72

<u>Number of girls in a group that has 16 boys = 18</u>

<u>There are 18 girls in a group that has 16 boys.</u>

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Work Shown:

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We multiply each term by 0.2, aka 1/5, to get the next term.

Since -1 < r < 1 is true, we can use the infinite geometric sum formula below

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As a sort of "check", we can add up partial sums like so

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and so on. The idea is that each time we add on a new term, we should be getting closer and closer to 375. I put "check" in quotation marks because it's probably not the rigorous of checks possible. But it may give a good idea of what's going on.

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Side note: If the common ratio r was either r < -1 or r > 1, then the terms we add on would get larger and larger. This would mean we don't approach a single finite value with the infinite sum.

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