A scientist has two solutions which she labeled Solution A and Solution B. Each solution contains salt. She knows that Solutions $$ A $$ is $$ 60 \% $$ salt and Solution $$ B $$ is $$ 90 \% $$ salt. She wants to obtain a $$ 60 $$ ounce mixture of the two solutions that is $$ 80 \% $$ salt. How many ounces of each solution should she use?

Question

A scientist has two solutions which she labeled Solution A and Solution B. Each solution contains salt. She knows that Solutions $$ A $$ is $$ 60 \% $$ salt and Solution $$ B $$ is $$ 90 \% $$ salt. She wants to obtain a $$ 60 $$ ounce mixture of the two solutions that is $$ 80 \% $$ salt. How many ounces of each solution should she use?

Macdonald Morgan · Accepted Answer

no. of  oz of  Solution A = xno. of  oz of  Solution B = y x + y = 600.6x + 0.9y = 0.8*60 Solve the following system: $$\left \{ \begin{array} { l } { y + x = 60 } \ { 0.9 y + 0.6 x = 48 } \end{array} ight .$$Express the system in standard form: $$\left \{ \begin{array} { l } { x + y = 60 } \ { 0.6 x + 0.9 y = 48 } \end{array} ight .$$Subtract $$ 0.6 	imes $$ (equation $$ 1 $$ ) from equation $$ 2$$ $$\left \{ \begin{array} { l } { x + y = 60 } \ { 0 x + 0.3 y = 12 } \end{array} ight .$$Divide equation $$ 2 $$ by $$ 0.3 $$ : $$\left \{ \begin{array} { l } { x + y = 60 } \ { 0 x + y = 40 } \end{array} ight .$$Subtract equation $$ 2 $$ from equation $$ 1 $$ : $$\left \{ \begin{array} { l } { x + 0 y = 20 } \ { 0 x + y = 40 } \end{array} ight .$$Answer: $$ \left \{ \begin{array} { l } { x = 20 } \ { y = 40 } \end{array} ight .$$  no. of  oz of  Solution A = 20no. of  oz of  Solution B = 40

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