Lesson 15: Practice Problems

Problem 1

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.

Problem 2

Decide which story can be represented by the system of equations $y = x + 6$ and $x + y = 100$ . Explain your reasoning.

Diego’s teacher writes a test worth 100 points. There are 6 more multiple choice questions than short answer questions.
Lin and her younger cousin measure their heights. They notice that Lin is 6 inches taller, and their heights add up to exactly 100 inches.

Problem 3

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.

Write a system of equations that describes Clare 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.
Solve the system. What does your solution mean?

Problem 4 From Unit 4 Lesson 14

Solve: ${\begin{cases} y = 6 x - 8 \\ y = - 3 x + 10 \end{cases}$

Problem 5 From Unit 4 Lesson 13

Two lines intersecting in the first quadrant. One is a positive slope, the other is negative.

Estimate the coordinates of the point where the two lines meet.
Choose two equations that make up the system represented by the graph.
1. $y = \frac{5}{4} x$
2. $y = 6 - 2.5 x$
3. $y = 2.5 x + 6$
4. $y = 6 - 3 x$
5. $y = 0.8 x$
Solve the system of equations and confirm the accuracy of your estimate.