Amy and Simon each bought a pair of shorts and some T-shirts. Each pair of shorts cost the same amount, and each T-shirt cost the same amount.

• -Amy paid $60 for 11 pair of shorts and 22 T-shirts.

• -Simon paid $75 for 11 pair of shorts and 33 T-shirts.

What was the cost, in dollars, of 11 pair of shorts?

Enter your answer in the box.

(a)  

This question has four parts. 

A student wrote the equation shown.

$$x^y=z$$

Part A

What is the value of z in the equation when x=3 and y=4? Show or explain how you got your answer.

Enter your answer and your work or explanation in the space provided.

Part B

What is the value of x in the equation when y=3 and z=125? Show or explain how you got your answer.

Enter your answer and your work or explanation in the space provided.

Part C

The student rewrote the equation as shown.

$$\sqrt[y]{z}=x$$

Is the value of x a rational number when y=2 and z=2? Explain your reasoning.

Enter your answer and your explanation in the space provided.

Part D

Write an integer value of y and an integer value of z that make the equation true when x=8. Show or explain how you got your answers.

Enter your answers and your work or explanation in the space provided.

Solve the system of equations.

$$y=2x-4$$

$$3y=2x$$

Drag and drop a number into each appropriate box to complete the ordered pair that represents the solution to the system of equations. Each number may be used once, more than once, or not at all.

(​ (a)   , ​ (b)   )