Question

At the end of the summer, Jeff discovers that his radiator antifreeze solution has dropped below the safe level. If the radiator contains 4 gallons of a 25% solution, how many gallons of pure antifreeze must he add to bring it up to a desired 50% solution?
___ Gallons

Answer 1

$\bf \begin{array}{lccclll} &amount&concentration& \begin{array}{llll} concentration\\ amount \end{array}\\ &-----&-------&-------\\ \textit{current sol'n}&4&0.25&1.00\\ \textit{pure sol'n}&x&1.00&1.00x\\ -----&-----&-------&-------\\ mixture&y&0.5&0.5y \end{array}$

notice, again, we use the decimal format of the percentage, 25% is just 25/100 or 0.25 and so on

so.. hmmm the quantities, of 4 + x, must add up to y, thus
4 + x = y

and their concentration amount, must add up as well

1.00 + x = 0.5y

thus    $\bf \begin{cases} 4+x=\boxed{y}\\ 1+x=0.5y\\ ----------\\ 1+x=0.5\left( \boxed{4+x} \right) \end{cases}$

solve for "x"