3 years ago

there are 4/7 as many girls as there are boys. There are 66 students in the fifth grade. How many students are girls?

Mathematics

1 answer:

zhenek [66]3 years ago

5 0

My guess is 24 girls.

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In the diagram, GH bisects ∠FGI.

Diano4ka-milaya [45]

An angle bisector divides the angle into equal halves.

The value of x is 20
FGH = HGI = 35
FGI = 70

From the question, we understand that GH bisects FGI.

This means that:

$< fgh \: = < hgi$

So, we have:

$2x - 5 = 3x - 25$

Collect like terms

$3x - 2x = 25 - 5$

Evaluate like terms

$x = 20$

From the question

$< fgh \: = 2x - 5$

Substitute 20 for x

$< fgh \: = 2 \times 20 - 5$

$< fgh \: = 35$

Recall that:

$< fgh \: = < hgi$

This means that:

$< hgi \: = 35$

The measure of FGI is the sum of both angles.

So, we have:

$< fgi \: = 35 + 35$

$< fgi = 70$