Biz \(x\) ni bizga kerak bo'ladigan 20% eritma miqdori bo'lishiga ruxsat berishdan boshlaymiz. Bu, o'z navbatida, aralashtirishni tugatgandan so'ng, bizda 35% eritmaning \(x + 20\)gallon bo'lishini anglatadi.

Keyin asosiy so'z tenglamasi,

\[\left( \begin{array}{c}{\mbox{Amount of acid}}\\ {\mbox{in 20% solution}}\end{array} \right) + \left( \begin{array}{c}{\mbox{Amount of acid}}\\ {\mbox{in 42% solution}}\end{array} \right) = \left( \begin{array}{c}{\mbox{Amount of acid}}\\ {\mbox{in 35% solution}}\end{array} \right)\]

Biz bilamizki, eritmadagi kislota miqdori = Eritmaning foizi X Eritma hajmi. Bu quyidagi so'z tenglamasini beradi.

\[\left( {0.20} \right)\left( \begin{array}{c}\,\,{\mbox{Volume of}}\\ {\mbox{20% solution}}\end{array} \right) + \left( {0.42} \right)\left( \begin{array}{c}\,\,{\mbox{Volume of}}\\ {\mbox{42% solution}}\end{array} \right) = \left( {0.35} \right)\left( \begin{array}{c}\,\,{\mbox{Volume of}}\\ {\mbox{35% solution}}\end{array} \right)\]

2-qadam

Shunday qilib, barcha ma'lum ma'lumotlarni ulash \(x\) uchun hal qilishimiz mumkin bo'lgan quyidagi tenglamani beradi.

\[\begin{align*}0.2x + \left( {0.42} \right)\left( {20} \right) & = 0.35\left( {x + 20} \right)\\ 0.2x + 8.4 & = 0.35x + 7\\ 0.15x & = 1.4\\ x & = 9.33\end{align*}\]

Shunday qilib, bizga 9,33 gallon 20% kislota eritmasi kerak bo'ladi.