Q: A company produces two types of granola bars: Regular and Protein. Each Regular bar requires $$2$$ minutes to make and each Protein bar requires $$3$$ minutes. If the company can spend at most $$60$$ minutes making bars per day and wants to make a total of $$25$$ bars, which system of equations models this situation?

$$\begin{cases} r + p = 25 \\ 2r + 3p = 60 \end{cases}$$

Q: Which of the following systems represents the scenario: 'The sum of two numbers is $$40. $$One number is $$8$$ more than twice the other'?

$$\begin{cases} x + y = 40 \\ x = 2y + 8 \end{cases}$$

Q: A chemist needs to mix a $$30\%$$ acid solution with a $$10\%$$ acid solution to obtain $$40$$ liters of a $$20\%$$ acid solution. Which system of equations models this problem?

$$\begin{cases} x + y = 40 \\ 0.3x + 0.1y = 0.2 \times 40 \end{cases}$$

Q: A store mixes $$x$$ pounds of M&M’s at $$\2.00$ per pound with y$ pounds of trail mix at $$\$$1.50$$ per pound to make $$50$$ pounds of party mix worth $$\1.80$ per pound. Which system of equations models this situation?

$$\begin{cases} x + y = 50 \\ 2x + 1.5y = 1.8 \times 50 \end{cases}$$

Question 1

A company produces two types of granola bars: Regular and Protein. Each Regular bar requires $$2$$ minutes to make and each Protein bar requires $$3$$ minutes. If the company can spend at most $$60$$ minutes making bars per day and wants to make a total of $$25$$ bars, which system of equations models this situation?

Accepted Answer

$$\begin{cases} r + p = 25 \ 2r + 3p = 60 \end{cases}$$

Question 2

A store sells pens for $$\1.20$ each and notebooks for $$\$$2.50$$ each. If a customer buys $$10$$ items and spends $$\19.60$, how many pens did they buy?

Accepted Answer

6

Question 3

Which of the following systems represents the scenario: 'The sum of two numbers is $$40. $$One number is $$8$$ more than twice the other'?

Accepted Answer

$$\begin{cases} x + y = 40 \ x = 2y + 8 \end{cases}$$

Question 4

A chemist needs to mix a $$30\%$$ acid solution with a $$10\%$$ acid solution to obtain $$40$$ liters of a $$20\%$$ acid solution. Which system of equations models this problem?

Accepted Answer

$$\begin{cases} x + y = 40 \ 0.3x + 0.1y = 0.2 	imes 40 \end{cases}$$

Question 5

A company’s fixed cost for producing widgets is $$\1200$. Each widget costs $$\$$3 to $$produce and sells for $$\7$. How many widgets must be sold to break even?

Accepted Answer

300

Question 6

A triangle has angles such that the largest angle is $$90^\circ$$ more than the smallest, and the middle angle is $$30^\circ$$ more than the smallest. What are the measures of the three angles?

Accepted Answer

$$20^\circ, 50^\circ, 110^\circ$$

Question 7

A store manager wants to mix nuts worth $$\5$ per pound with raisins worth $$\$$3$$ per pound to get $$40$$ pounds of a mixture worth $$\4$ per pound. How many pounds of nuts should be used?

Accepted Answer

20

Question 8

A boat travels $$24$$ miles downstream in $$2$$ hours and the same distance upstream in $$3$$ hours. What is the speed of the current?

Accepted Answer

2$$\ 	ext{mph}$$

Question 9

A drama club sold $$311$$ tickets. Student tickets cost $$\0.50$ and non-student tickets cost $$\$$1.50. If $$total receipts were $$\385.50$, how many student tickets were sold?

Accepted Answer

81

Question 10

Which of the following is the correct interpretation of the break-even point in a cost-revenue analysis?

Accepted Answer

The point where total revenue equals total cost.

Question 11

A store mixes $$x$$ pounds of M&M’s at $$\2.00$ per pound with y$ pounds of trail mix at $$\$$1.50$$ per pound to make $$50$$ pounds of party mix worth $$\1.80$ per pound. Which system of equations models this situation?

Accepted Answer

$$\begin{cases} x + y = 50 \ 2x + 1.5y = 1.8 	imes 50 \end{cases}$$

Question 12

If $$x = 4 + 2y$$ and $$x + y = 25$$, what is the value of $$y$$?

Accepted Answer

7

Question 13

A company’s cost function is $$C(x) = 2000 + 1.5x$$ and its revenue function is $$R(x) = 4x. $$What is the break-even quantity?

Accepted Answer

800

Question 14

A student solves the system $$\begin{cases} x + y = 10 \ 2x - y = 3 \end{cases}$$ and finds $$x = 4.33. $$What is the value of $$y$$?

Accepted Answer

5.67

Question 15

A car rental company charges a flat fee of $$\50$ plus $$\$$0.20$$ per mile driven. If a customer paid $$\90$, how many miles did they drive?

Accepted Answer

200

Question 16

Which method is most efficient for solving a system where one equation is already solved for a variable?

Accepted Answer

Substitution method

Systems of Equations and Problem Solving in Intermediate Algebra

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