Asked by peter
there were 825 pupils in a school. 52 percent were boys. more boys joined the school and the percentage of boys became 64 percent of the new total. how many boys joined the school?
Answers
Answered by
Bosnian
52 % of 825 = ( 52 / 100 ) * 825 = 52 * 825 / 100 = 42900 / 100 = 429 boys
When more boys joined the school numbers of boys will be:
429 + x
total number of pupils will be 825 + x
( 429 + x ) / ( 825 + x ) = 64 % = 64 / 100 = 0.64
( 429 + x ) / ( 825 + x ) = 0.64 Multiply both sides by 825 + x
429 + x = 0.64 * ( 825 + x )
429 + x = 0.64 * 825 + 0.64 * x
429 + x = 528 + 0.64 x Subtract 0.64 x to both sides
429 + x - 0.64 x = 528 + 0.64 x - 0,64 x
429 + 0.36 x = 528 Subtract 429 to both sides
429 + 0.36 x - 429 = 528 - 429
0.36 x = 99 Divide both sides by 0.36
x = 99 / 0.36 = 275 boys
Proof:
When 275 boys joined the school numbers of boys will be 429 + 275 = 704 boys
Total number of pupils will be 825 + 275 = 1100 pupils
704 / 1100 = 0.64 = 64 %
When more boys joined the school numbers of boys will be:
429 + x
total number of pupils will be 825 + x
( 429 + x ) / ( 825 + x ) = 64 % = 64 / 100 = 0.64
( 429 + x ) / ( 825 + x ) = 0.64 Multiply both sides by 825 + x
429 + x = 0.64 * ( 825 + x )
429 + x = 0.64 * 825 + 0.64 * x
429 + x = 528 + 0.64 x Subtract 0.64 x to both sides
429 + x - 0.64 x = 528 + 0.64 x - 0,64 x
429 + 0.36 x = 528 Subtract 429 to both sides
429 + 0.36 x - 429 = 528 - 429
0.36 x = 99 Divide both sides by 0.36
x = 99 / 0.36 = 275 boys
Proof:
When 275 boys joined the school numbers of boys will be 429 + 275 = 704 boys
Total number of pupils will be 825 + 275 = 1100 pupils
704 / 1100 = 0.64 = 64 %
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