Q: A chemist needs to prepare 10 oz of a 12.5% hydrochloric acid solution by mixing a 5% solution and a 20% solution. Let $$x be $$the ounces of 5% solution and $$y be $$the ounces of 20% solution. Which system of equations correctly models this situation?

$$x + y = 10 \\ 0.05x + 0.20y = 1.25$$

Question 1

A chemist needs to prepare 10 oz of a 12.5% hydrochloric acid solution by mixing a 5% solution and a 20% solution. Let $$x be $$the ounces of 5% solution and $$y be $$the ounces of 20% solution. Which system of equations correctly models this situation?

Accepted Answer

$$x + y = 10 \ 0.05x + 0.20y = 1.25$$

Question 2

If $$x$$ ounces of 5% hydrochloric acid and $$y$$ ounces of 20% hydrochloric acid are mixed to make 10 oz of a 12.5% solution, what is the value of $$y$$?

Accepted Answer

$$y = 5$$

Question 3

After solving the system $$x + y = 10$$ and $$0.05x + 0.20y = 1.25$$, what is the value of $$x$$?

Accepted Answer

$$x = 5$$

Question 4

A car travels 250 km in the same time that a truck travels 225 km. If the car's rate is 8 km/hr faster than the truck's rate, what equation represents the relationship between their rates?

Accepted Answer

$$\frac{250}{x} = \frac{225}{y}$$ and $$x = y + 8$$

Question 5

Given the system $$250y = 225(y + 8)$$, what is the value of $$y$$?

Accepted Answer

$$y = 72$$

Question 6

What is the rate of the car in the distance-rate-time problem described, if the truck's rate is $$y km/hr$$?

Accepted Answer

$$x = y + 8$$

Question 7

If the truck's rate is 72 km/hr, what is the car's rate?

Accepted Answer

$$80 km/hr$$

Question 8

In a mixture problem, why do we multiply the equation $$0.05x + 0.20y = 1.25 by 100 $$before solving?

Accepted Answer

To eliminate decimals and make the coefficients easier to work with

Question 9

A pharmacist needs to mix a 5% saline solution and a 20% saline solution to get 10 oz of a 12.5% solution. How much pure saline will be in the final mixture?

Accepted Answer

$$1.25 oz$$

Question 10

Which of the following best describes the elimination method used to solve the system $$5x + 20y = 125$$ and $$x + y = 10$$?

Accepted Answer

Multiply the second equation by $$-5$$ and add to the first to eliminate $$x$$

Question 11

If a solution is made by mixing equal parts of a 5% and a 20% hydrochloric acid solution, what will be the concentration of the resulting mixture?

Accepted Answer

$$12.5\%$$

Question 12

A car and a truck leave at the same time and travel for the same amount of time. The car travels 250 km, and the truck travels 225 km. If the car's speed is 8 km/hr faster, what is the time they both traveled?

Accepted Answer

$$\frac{250}{80}$$ hours

Question 13

Which step is NOT necessary when solving a mixture problem using two variables?

Accepted Answer

Convert all measurements to the metric system

Question 14

A solution contains 5 oz of 5% acid and 5 oz of 20% acid. What is the percent concentration of acid in the final 10 oz solution?

Accepted Answer

$$12.5\%$$

Question 15

If $$x$$ and $$y$$ are the amounts of two solutions mixed to form a new solution, and $$x + y = 10$$, what does this equation represent in the context of a mixture problem?

Accepted Answer

The total volume of the final solution

Question 16

In the distance-rate-time problem, what formula is used to relate distance, rate, and time?

Accepted Answer

$$d = rt$$

Question 17

A chemist wants to make 10 oz of a 12.5% solution using only 5% and 20% solutions. If $$x is $$the amount of 5% solution, which equation gives the total amount of pure acid in the mixture?

Accepted Answer

$$0.05x + 0.20y = 1.25$$

Solving Mixture and Distance-Rate-Time Problems Using Two Variables 3.3

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