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Caste 4 | Men | Sangily 4
Question 9
his question is worth 2 credits.
ne dagram bellow shows line AB, line CD, and line Er,
lentify two lines on the diagram that appear to be perpendicular to each other. vplain how you determined your answer.

Caste $4$ | Men | Sangily $4$ $\newline$ Question $9$ $\newline$ his question is worth $2$ credits. $\newline$ ne dagram bellow shows line AB, line CD, and line Er, $\newline$ lentify two lines on the diagram that appear to be perpendicular to each other. vplain how you determined your answer.

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Weighted averages: word problems

Full solution

Q. Caste

4

| Men | Sangily

4

\newline

Question

9

\newline

his question is worth

2

credits.

\newline

ne dagram bellow shows line AB, line CD, and line Er,

\newline

lentify two lines on the diagram that appear to be perpendicular to each other. vplain how you determined your answer.

Identify Total Acetone: Step $1$ : Identify the total amount of acetone in the initial $100$ gallons of $14\%$ solution. $\newline$ Calculation: $100$ gallons $\times 14\% = 100 \times 0.14 = 14$ gallons of acetone.
Set Up Equation: Step $2$ : Set up the equation to find the amount of $9$ % solution $x$ gallons) needed to reach a $10$ % concentration in the final mixture. $\newline$ Expression for acetone in the added $x$ gallons: $x \times 9\% = x \times 0.09$ . $\newline$ Expression for total acetone in the final mixture: $14$ gallons (from step $1$ ) + $0.09x$ gallons. $\newline$ Expression for total volume of the final mixture: $100$ gallons + $x$ gallons. $\newline$ Final concentration target: $10\%$ of $(100 + x)$ gallons. $\newline$ Equation: $14 + 0.09x = 0.10(100 + x)$ .
Solve Equation: Step $3$ : Solve the equation from Step $2$ . $\newline$ Distribute and simplify the equation: $14 + 0.09x = 10 + 0.10x$ . $\newline$ Rearrange to isolate $x$ : $14 - 10 = 0.10x - 0.09x$ . $\newline$ Simplify: $4 = 0.01x$ . $\newline$ Solve for $x$ : $x = 4 / 0.01 = 400$ gallons.

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