Question

part a
a scientist needs 10 liters of a 20% acid solution for an experiment, but she has only a 5% solution and a 40% solution. about how many liters of the 5% and the 40% solutions should the scientist mix to get the solution she needs?
choose the equation to match the situation.
a ((0.20)(10) = 0.05x + 0.40x)
b ((0.20)(10) = 0.05x + 0.40(10 - x))
c ((0.20)(10) = 0.05(10) + 0.40(10 - x))
d ((0.20)(10) = 0.05(10 - x) + 0.40(10 - x))
part b
round the answers to the nearest tenth.
she should mix (square) liters of 5% solution with (square) liters of 40% solution.

Explanation:

Part A

Step1: Understand the mixture problem

Let \( x \) be the liters of 5% solution. Then the liters of 40% solution is \( 10 - x \) (since total is 10 liters). The amount of acid in the 20% solution (total) is \( 0.20\times10 \). The amount of acid in 5% solution is \( 0.05x \) and in 40% solution is \( 0.40(10 - x) \). So the equation is \( 0.20(10)=0.05x + 0.40(10 - x) \), which is option B.

Step2: Confirm the equation structure

Left side: acid in final solution (\( 0.20\times10 \)). Right side: acid from 5% (\( 0.05x \)) plus acid from 40% (\( 0.40(10 - x) \)). This matches option B.

Step1: Solve the equation from Part A

Start with \( 0.20\times10=0.05x + 0.40(10 - x) \). Calculate left side: \( 2 = 0.05x + 4 - 0.40x \).

Step2: Combine like terms

Simplify right side: \( 2 = 4 - 0.35x \). Subtract 4 from both sides: \( 2 - 4=-0.35x \), so \( -2=-0.35x \).

Step3: Solve for \( x \)

Divide both sides by \( -0.35 \): \( x=\frac{-2}{-0.35}\approx5.714 \). Then liters of 40% solution is \( 10 - 5.714\approx4.286 \). Round to nearest tenth: \( x\approx5.7 \), \( 10 - x\approx4.3 \).

Answer:

B. \( (0.20)(10) = 0.05x + 0.40(10 - x) \)

Part B