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ss7ja [257]
3 years ago
6

Of the students attending a school party, 60% of the students are girls, and 40% of the students like to dance. After these stud

ents are joined by 20 more boy students, all of whom like to dance, the party is now 58% girls. How many students now at the party like to dance?
Mathematics
1 answer:
elena-s [515]3 years ago
7 0

Answer:

252 students at the party like to dance

Step-by-step explanation:

Given:

60% of the students are girls

40% of the students like to dance

20 more boy students

Percentage of the girls in the party = 58%

To Find:

How many students now at the party like to dance=?

Solution:

Let the number of girls be g.

Let the number of total people originally be t.

We know that

\frac{g}{t}=\frac{60}{100}

\frac{g}{t}=\frac{3}{5}----------------------------------(1)

We also know that

\frac{g}{t+20}=\frac{58}{100}

\frac{g}{t+20}=\frac{29}{50}-----------------------------(2)

We now have a system of equation from (1) and (2)

3t=5g

g = \frac{3t}{5} ------------------------(3)

50g=29t+580------------------------(4)

Substituting 3 in 4, we get

50(\frac{3t}{5})=29t+580

(\frac{150t}{5})=29t+580

30t =29t+580

30t -29t = 580

t =589

So originally there was 580 students

In this 580 students 40% liked to dance

Then the number of students liked to dance =

=> 40\% \text{of} 580

=>\frac{40}{100} \times 580

=>0.4 \times 580

=> 232

We also know that with these people, 20 boys joined, all of whom like to dance.

Now the number of students like to dance  = 232+20 = 252 students

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