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

Step-by-step explanation:

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

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

$(x+4)(0.30)=0.80+1.00x\\0.30x+1.20=0.80+1.00x\\.\qquad \quad 1.20=0.80+0.70x\\.\qquad \quad 0.40=\qquad \quad 0.70x\\\\.\qquad \quad \dfrac{0.40}{0.70}=\qquad \quad \dfrac{0.70x}{0.70}\\\\.\qquad \quad 0.57=\qquad \qquad x$