Lesson 15: Writing Systems of Equations | Unit 4: Linear Equations and Linear Systems

Open Ended

Kiran and his cousin work during the summer for a landscaping company. Kiran's cousin has been working for the company longer, so his pay is 30% more than Kiran's. Last week his cousin worked 27 hours, and Kiran worked 23 hours. Together, they earned $493.85. What is Kiran's hourly pay? Explain or show your reasoning.

Multiple Choice

Clare and Noah play a game in which they earn the same number of points for each goal and lose the same number of points for each penalty. Clare makes 6 goals and 3 penalties, ending the game with 6 points. Noah earns 8 goals and 9 penalties and ends the game with -22 points. Which of the following systems of equations describes Clare's and Noah's outcomes? Use x to represent the number of points for a goal and y to represent the number of points for a penalty.

• 6x + 3y = 6, 8x + 9y = -22
• {6x - 3y = 6, 8x - 9y = -22}
• 6x - 3y = 12, 8x - 9y = -10
• 6x - 3y = 0, 8x - 9y = -30

Multiple Choice

Clare and Noah play a game in which they earn the same number of points for each goal and lose the same number of points for each penalty. Clare makes 6 goals and 3 penalties, ending the game with 6 points. Noah earns 8 goals and 9 penalties and ends the game with -22 points. Solve the system of equations you wrote in the previous question. What does your solution mean?

• Each goal is worth 2 points and each penalty costs 3 points.
• Each goal is worth 4 points and each penalty costs 6 points.
• Each goal is worth 5 points and each penalty costs 4 points.
• Each goal is worth 3 points and each penalty costs 5 points.

Multiple Choice

Andre’s school orders some new supplies for the chemistry lab. The online store shows a pack of 10 test tubes that costs $4 less than a set of nested beakers. Which equation shows the cost of a pack of 10 test tubes, $$t$$ , in terms of the cost of a set of nested beakers, $$b$$ ?

• t = b + 4
• t = b - 10
• t = b - 4
• t = 4b

Multiple Choice

Andre’s school orders some new supplies for the chemistry lab. In order to fully equip the lab, the school orders 12 sets of beakers and 8 packs of test tubes. The school office receives a bill for the supplies in the amount of $348. Which equation with $$t$$ and $$b$$ describes this situation?

• 12b + 8t = 348
• 8b + 12t = 348
• 10b + 6t = 348
• 12b + 10t = 348

Multiple Choice

Andre’s school orders some new supplies for the chemistry lab. Since $$t$$ is in terms of $$b$$ in the first equation, this expression can be substituted into the second equation where $$t$$ appears. Which of the following equations shows this substitution?

• t = b^2 where b is squared in the second equation.
• t = b + c where c is a constant value.
• t = f(b) where f(b) is the expression derived from the first equation.
• t = g(b) where g(b) is unrelated to the first equation.

Multiple Choice

Andre’s school orders some new supplies for the chemistry lab. Solve the equation for $$b$$ : 3b + 5 = 20

• 0
• 10
• 5
• 15

Multiple Choice

How much did the school pay for a set of beakers?

• $50
• $100
• $200
• Unknown

Open Ended

Diego’s history teacher writes a test with 26 questions for the class. The test is worth 123 points and has two types of questions: multiple choice worth 3 points each and essays worth 8 points each. How many essay questions are on the test? Explain or show your reasoning.

Multiple Choice

The school designed their vegetable garden to have a perimeter of 32 feet, with the length measuring 2 feet more than twice the width. Using $$\ell$$ to represent the length of the garden and $$w$$ to represent its width, which of the following systems of equations describes this situation?

• \ell = 2w + 2, 2(\ell + w) = 32
• $\ell = 3w, 2(\ell + w) = 32$
• $\ell = w + 4, 2(\ell + w) = 40$
• $\ell = 2w - 2, 2(\ell + w) = 20$