Q: A chemist needs to mix a 10% acid solution with a 60% acid solution to obtain 50 milliliters of a 30% acid solution. Which system of equations correctly models this situation, where $$x is $$the amount of 10% solution and $$y is $$the amount of 60% solution?

$$\begin{cases} x + y = 50 \\ 0.10x + 0.60y = 0.30 \times 50 \end{cases}$$

Q: A pharmacist needs to mix a 20% saline solution with a 50% saline solution to obtain 100 mL of a 30% solution. Which equation represents the amount of pure saline in the final mixture?

$$0.20x + 0.50y = 0.30 \times 100$$

Q: Which of the following systems would you use to solve for the amount of two solutions needed to create a mixture of a certain concentration?

$$\begin{cases} x + y = \text{total volume} \\ c_1x + c_2y = c_m \times \text{total volume} \end{cases}$$

Question 1

A chemist needs to mix a 10% acid solution with a 60% acid solution to obtain 50 milliliters of a 30% acid solution. Which system of equations correctly models this situation, where $$x is $$the amount of 10% solution and $$y is $$the amount of 60% solution?

Accepted Answer

$$\begin{cases} x + y = 50 \ 0.10x + 0.60y = 0.30 	imes 50 \end{cases}$$

Question 2

Suppose you invest $$25,000, part at 9% simple interest and the remainder at 12%. If the total yearly interest is 2$$,550, how much was invested at 9%?

Accepted Answer

$$15,000$$

Question 3

A rectangular lot is fenced on three sides. The length is fenced with material costing $$20 per foot, and the two widths are fenced with material costing 8 $$per foot. If the perimeter is 360 feet and the total cost is $3,280, what is the width of the lot?

Accepted Answer

$$80$$ feet

Question 4

Which equation represents the total interest earned from investing $$x$$ dollars at 9% and $$y$$ dollars at 12% for one year?

Accepted Answer

$$0.09x + 0.12y = 2550$$

Question 5

If the sum of the average times spent socializing for men and women is 138 minutes, and the difference is 8 minutes (women socialize more), what is the average time men spend socializing?

Accepted Answer

$$65$$ minutes

Question 6

A pharmacist needs to mix a 20% saline solution with a 50% saline solution to obtain 100 mL of a 30% solution. Which equation represents the amount of pure saline in the final mixture?

Accepted Answer

$$0.20x + 0.50y = 0.30 	imes 100$$

Question 7

A rectangular lot has a perimeter of 360 feet and is fenced on three sides. If the length is $$x$$ and the width is $$y$$, which equation represents the perimeter?

Accepted Answer

$$x + 2y = 360$$

Question 8

If $$I = Pr is $$the formula for simple interest, what is the interest earned on $$\8$$,000$$ invested at 5$$\%$ for one year?

Accepted Answer

$$400$$

Question 9

A chemist mixes 30 mL of a 10% acid solution with 20 mL of a 60% acid solution. What is the concentration of the resulting 50 mL solution?

Accepted Answer

$$30\%$$

Question 10

Which of the following systems would you use to solve for the amount of two solutions needed to create a mixture of a certain concentration?

Accepted Answer

$$\begin{cases} x + y = 	ext{total volume} \ c_1x + c_2y = c_m 	imes 	ext{total volume} \end{cases}$$

Question 11

A student invests $$\2$$,000$$ at 4$$\%$$ and $$\$$3,000 at$$ $$6\%. $$What is the total interest earned in one year?

Accepted Answer

$$180$$

Question 12

If the total cost of fencing a rectangular lot is $$C = 20x + 8(2y)$$, where $$x is $$the length and $$y is $$the width, what is the cost to fence a lot with $$x = 100$$ feet and $$y = 80$$ feet?

Accepted Answer

$$3,280$$

Question 13

A chemist wants to create 100 mL of a 25% solution using 10% and 40% solutions. Let $$x be $$the amount of 10% solution and $$y$$ the amount of 40% solution. Which equation represents the total amount of solution?

Accepted Answer

$$x + y = 100$$

Question 14

If $$x is $$the amount invested at 9% and $$y at 12$$%, and the total investment is $$25,000$$, which equation represents this relationship?

Accepted Answer

$$x + y = 25,000$$

Question 15

A chemist mixes $$x mL of a 20$$% solution and $$y mL of a 50$$% solution to get 100 mL of a 30% solution. If $$x = 66.67$$, what is $$y$$?

Accepted Answer

$$33.33$$

Systems of Linear Equations and Inequalities: Applications and Problem Solving

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