Question

At Melville High School 20% of the girls and 50% of the boys went to a basketball game. Since 40% of all the students were girls, what percent of all students went to the game?

Answer 1

Answer:

$38\%$

Step-by-step explanation:

$Let\ total\ number\ of\ students=x\\\\Number\ of\ Girls=40\%\ of\ x\\\\Number\ of\ girls=\frac{40}{100}\times x=0.4x\\\\Number\ of\ boys=x-0.4x=0.6x$

Students went to game:

$Girls\ went\ to\ game=20\%\ of\ 0.4x\\\\Girls\ went\ to\ game=\frac{20}{100}\times 0.4x=0.2\times 0.4x=0.08x\\\\Boys\ went\ to\ game=50\%\ of\ 0.6x\\\\Boys\ went\ to\ game=\frac{50}{100}\times 0.6x=0.3x\\\\Students\ went\ to\ game=Girls\ went\ to\ game+Boys\ went\ to\ game\\\\Students\ went\ to\ game=0.3x+0.08x=0.38x\\\\Percentage\ of\ students\ went\ to\ game=\frac{0.38x}{x}\times 100=38\%$