Question

Angela plays soccer and golf for a total of 125 minutes every day. She plays soccer for 45 minutes longer than she plays golf. Part A: Write a pair of linear equations to show the relationship between the number of minutes Angela plays soccer (x) and the number of minutes she plays golf (y) every day. (5 points) Part B: How much time does Angela spend playing golf every day? Show your work. (3 points) Part C: Is it possible for Angela to have spent 80 minutes playing soccer if she plays for a total of exactly 125 minutes and plays soccer for 45 minutes longer than she plays golf? Explain your reasoning. (2 points)

Answer 1

Answer:

Part A) x + y=125, y = x +45

Part B) 85 minutes

Part C) Not possible

Step-by-step explanation:

Given that Angela plays soccer and golf for a total of 125 minutes everyday.

Number of minutes she plays golf = x minutes

Number of minutes she plays soccer = y minutes

Part A:

Total time she plays golf and soccer is 125 minutes.

$x+y=125 ...... (1)$

Angela plays Soccer for 45 minutes longer than she plays golf i.e.

$y = x+45 ....... (2)$

The pair of linear equations are:

$x + y=125, y = x +45$

Part B:

Let us solve the linear equations (1) and (2):

Putting value of y from equation (2) into equation (1):

$x+x+45=125 \\\Rightarrow 2x+45=125\\\Rightarrow 2x=80\\\Rightarrow x=40$

Putting value of x in equation (2):

$y = 40 +45 = 85\ minutes$

Angela plays golf for 85 minutes daily.

Part C:

Given that

Angela spends 80 minutes on soccer.

Total Time = 125 minutes

$\Rightarrow$ Time spent on golf = 125 - 80 = 45 minutes

Time spent on soccer longer than golf = 80 - 45 = 35 minutes $\neq$ 45 minutes

Hence, it is not possible for Angela to have spent 80 minutes playing soccer if she plays for a total of exactly 125 minutes and plays soccer for 45 minutes longer than she plays golf.

So, the answers are:

Part A) x + y=125, y = x +45

Part B) 85 minutes

Part C) Not possible