Question

a student played a computer game 500 times and won 370 of these game. he then won the next "x" games and lost none. he has now won 75% of fhe games he has played. find the value of "x"

Answer 1

So, this is a proportion problem. If we express 75% as a fraction (3/4ths), we have:

$\frac{370+x}{500+x}=\frac{3}{4}$

Since he won all of his games, we add the number won (x), to the number previously won and divide it by the total games played which is just the previous games played plus the number of current games played, so since he lost no games we still add x to the denominator as well. Solving this gives us:

$4(370+x)=3(500+x) \implies\\ 1480+4x=1500+3x \implies \\ x=20$

That x value is 20.