Question

CHEMISTRY You combine $2$ solution to form a mixture that is $40\%$ acid. One solution is $20\%$ acid and the other is $50\%$ acid. If you have $90$ milliliters of the mixture, how much of each solution was used to create the mixture?

• A. $20$ mLof solution $A$ and $80$ mL of solution $B$ were used.
• B. $80$ mLof solution $A$ and $70$ mL of solution $B$ were used.
• C. $30$ mL of solution $A$ and $60$ mL of solution $B$ were used.
• D. $40$ mLof solution $A$ and $70$ mL of solution $B$ were used.

Answer 1

Answer: (C)

$30$ mL of solution $A$ and $60$ mL of solution $B$ were used.

Algebraic model $x+y=90$ ......(1)
$0.2x+0.5y=36$ ......(2)
Solve equation (1) for $x$ and multiply each side of equation (2) by $10$, so that it contains only integers.

Then use substitution to solve the system.
$x=90-y$ .......(3)
$2x+5y=360$ ......(4)
$2(90-y)+5y=360$

Substitute $90-y$ for $x$ in equation (4), we get
$180-2y+5y=360$
$3y=180$
$y=60$

Solve for $y$.
$x=90-60=30$

Substitute $60$ for $y$ in equation (3).
$30$ mLof solution $A$ and $60$ mL of solution $B$ were used.