Question

If there are 400 cubic centimeters of a chemical in 1 liter of solution, how many cubic centimeters of water must be added to dilute it to a 25% solution?

Answer 1

keeping in mind that, in 1 liter, there are 1000 cm³, and that the concentration amount of the chemical for say 25% will be 0.25 of whatever the quantity is, so... we convert the percentage amounts to decimal formats.


`\bf \begin{array}{lccclll} &\stackrel{cm^3}{amount}&\stackrel{\textit{\% of chemical}}{concentration}&\stackrel{total~amount}{concentration}\\ &------&------&------\\ solution&1000&0.4&400\\ water&x&0&0x\\ ------&------&------&------\\ mixture&y&0.25&0.25y \end{array}`

so.. whatever "x" and "y" are, we know that 1000 + x = y.

and that 400 + 0x = 0.25y.

thus then


`\bf \begin{cases} 1000+x=\boxed{y}\\ 400+0x=0.25y\\ 400=0.25y\\ ----------\\ 400=0.25\left( \boxed{1000+x} \right) \end{cases} \\\\\\ 400=250+0.25x\implies 150=0.25x\implies \cfrac{150}{0.25}=x\implies 600=x`