280 oranges are divided among some boys and girls whose total number is 50 so that each boy gets 5 oranges and each girl get 7 oranges. the number of girls is?

Number of girls = 15.

Quick explanation

Let the number of boys be bbb and the number of girls be ggg.
You are told:

• Total children: b+g=50b+g=50b+g=50

• Total oranges: 5b+7g=2805b+7g=2805b+7g=280 (since each boy gets 5 and each girl gets 7)

From the first equation, b=50−gb=50-gb=50−g. Substitute into the second:

5(50−g)+7g=2805(50-g)+7g=2805(50−g)+7g=280

250−5g+7g=280250-5g+7g=280250−5g+7g=280

250+2g=280250+2g=280250+2g=280

2g=30⇒g=152g=30\Rightarrow g=152g=30⇒g=15

So there are 15 girls and therefore 35 boys.

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