Question

O (1,2) Question 9 (Essay Worth 10 points) (04.01. 04.02 HC) Max practices the piano and the guitar for a total of 150 minutes every day. He practices the guitar for 80 minutes longer than he practices the piano. Part A: Write a pair of linear equations to show the relationship between the number of minutes Max practices the guitar (x) and the number of minutes he practices the piano (y) every day. (5 points) Part B: How much time does Max spend practicing the piano every day? Show your work. (3 points) Part C: Is it possible for Max to have spent 125 minutes practicing the guitar if he practices for a total of exactly 150 minutes and practices the guitar for 80 minutes longer than he practices the piano? Explain your reasoning. (2 points) LED Source VC B I U S x x x E = 3 = Styles Normal ? Part A y = x + 80 uestion Question 1 (Answered) O

Answer 1

Let

x -----> the number of minutes He practices the guitar

y ----> the number of minutes he practices the piano

we know that

x+y=150 ------> equation A

x=y+80 -----> equation B

solve the system of equations

substitute equation B in equation A

(y+80)+y=150

solve for y

combine like terms

2y+80=150

2y=150-80

2y=70

y=35 minutes

Find the value of x

x=y+80

x=35+80

x=115 minutes

therefore

Part B: How much time does Max spend practicing the piano every day? -----> 35 minutes

Part C: Is it possible for Max to have spent 125 minutes practicing the guitar if he practices for a total of exactly 150 minutes and practices the guitar for 80 minutes longer than he practices the piano?

Is not possible, because the number of minutes He practices the guitar is 115 minutes