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# Need help

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75% of the passengers on a ferry were adults. 40% of the rest were girls. There were 168 more adults than boys. Some adults got off the ferry, after which 40% of the passengers were children. How many adults got off the ferry?

May 19, 2022

#1
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How many adults got off the ferry?

Hello Guest!

$$f=a+g+b\\ a=0.75f\\ 0.25f=b+g\\ a=b+168\\ g=0.4\cdot 0.25f\\ g+b=0,4(f-168)$$

$$g+b=0.25f=0.4(f-168)\\ 0.25f=0.4f-67.2\\ 0.15f=67.2\\ f=448\\ \color{blue}a=336$$

336 adults got off the ferry.

No!

I have to think again. !

May 19, 2022
edited by asinus  May 19, 2022
edited by asinus  May 19, 2022
#2
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How many adults got off the ferry?

Hello Guest!

$$f=a+g+b\\ a=0.75(a+g+b)\\ 0.25f=b+g\\ a=b+168\\ 0.4(f-x)=g+b\\ 0.25f=0.4f-0.4x$$

$$0.15f=0.4x\\x=0.375f\\ f=b+168+b+g\\ 4b+4g=2b+g+168\\2b+3g=168$$

to be continued



May 19, 2022
edited by asinus  May 19, 2022
edited by asinus  May 19, 2022
#3
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Let the total number of people on the ferry==T
0.25T ==children

0.40 * 0.25T ==0.10T are girls
0.25T - 0.10T ==0.15T are boys.
0.75T - 0.15T ==168
0.60T ==168

T ==168 / 0.60 ==280 people on the ferry.
0.10 x 280 ==28 girls on the ferry
0.15 x 280 ==42 boys on the ferry

28 + 42 ==70 children on the ferry
280 - 70 ==210 adults on the ferry
70 / 0.40 ==175 people remained

280 - 175 ==105 adults left the ferry, or 1/2 of adults left the ferry.

210 - 105 ==105 adults remained on the ferry
105 adults + 70 children ==175 people remained on the ferry.

May 19, 2022