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?

Answer 1

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 %