Question

A scientist needs 30% solution of acid. He has 4 liters of a 20% solution. How much pure acid does the scientist need to add to get the 30% solution?

PLEASE ANSWER USING A TABLE AND USING ONE VARIABLE ONLY.

Answer 1

Answer: 0.57 liters

Explanation:

Create a table. Multiply across and add down. The bottom row will result in the equation that needs to be solved:

`\begin {array}c&\underline{Quantity}&\underline{Percent}&\underline{Quantity * Percent}\\ Solution\ A&4\ liters&20\%\ =0.20&4(0.20)=0.80\\\underline{Solution\ B}&\underline{\qquad x\ \qquad}&\underline{100\%=1.00}&\underline{x(1.00)=1.00x\qquad }\\Mixture&x+4&30\%=0.30&\qquad \qquad =0.80+1.00x\\\end{array}`

`(x+4)(0.30)=0.80+1.00x\\0.30x+1.20=0.80+1.00x\\.\qquad \quad 1.20=0.80+0.70x\\.\qquad \quad 0.40=\qquad \quad 0.70x\\\\.\qquad \quad (0.40)/(0.70)=\qquad \quad (0.70x)/(0.70)\\\\.\qquad \quad 0.57=\qquad \qquad x`