How many quarts of pure antifreeze must be added to 5 quarts
of a 10% antifreeze solution to obtain a 40% antifreeze solution?
Here's another way to think of it:
The 5 quarts of 10% antifreeze contains (5)(0.10) = 0.5 quart of pure
antifreeze, (and the rest of the 5 quarts is 4.5 quarts of water,
which we aren't concerned with).
We are adding X quarts of pure antifreeze to the 0.5 quarts of pure
antifreeze (and water). So after pouring them together,
there will be X+0.5 quarts of pure antifreeze in the mixture. And
that will make 5+X quarts of liquid.
The equation is
Multiply both sides by (5+X)
Multiply through by 10 to clear the decimals.
Edwin