Question 4 Anastasia needs 40 milliliters of a $$ 38 \% $$ acid solution for a chemistry experiment. She has two acid solutions, A and B, that can be mixed together to form the solution. Solution A is $$ 30 \% $$ acid, and Solution B is $$ 40 \% $$ acid. How much of each solution should she use to create the mixture? She should use She should use Question Help: Milliliters of Solution A. Submit Question Jump to Answer

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Let $$ x $$ be the milliliters of Solution A and $$ y $$ be the milliliters of Solution B. We have two requirements:

1. Total volume:
$$
x + y = 40
$$

2. Total acid content:
$$
0.30x + 0.40y = 15.2
$$
(since $$ 0.38 \times 40 = 15.2 $$)

**Step 1.** Express $$ y $$ in terms of $$ x $$ from the total volume equation:
$$
y = 40 - x
$$

**Step 2.** Substitute $$ y = 40 - x $$ into the acid content equation:
$$
0.30x + 0.40(40 - x) = 15.2
$$

**Step 3.** Distribute $$ 0.40 $$ in the equation:
$$
0.30x + 16 - 0.40x = 15.2
$$

**Step 4.** Combine like terms:
$$
-0.10x + 16 = 15.2
$$

**Step 5.** Solve for $$ x $$:
$$
-0.10x = 15.2 - 16
$$
$$
-0.10x = -0.8
$$
$$
x = \frac{-0.8}{-0.10} = 8
$$

**Step 6.** Find $$ y $$ using $$ y = 40 - x $$:
$$
y = 40 - 8 = 32
$$

Anastasia should use $$ 8 $$ milliliters of Solution A and $$ 32 $$ milliliters of Solution B.
Anastasia should use 8 milliliters of Solution A and 32 milliliters of Solution B.

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