Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.

Question

Finn is trying to incorporate more exercise into his busy schedule. He has several short exercise routines he can complete at home. Last week, he worked out for a total of 67 minutes by doing 1 arm routine and 3 abdominal routines. This week, he has completed 1 arm routine and 1 abdominal routine and spent a total of 29 minutes exercising. How long does each routine last? An arm routine takes how many minutes to complete, and an abdominal routine takes how many minutes to complete.

Answer 1

r = minutes per arm exercise

b = minutes per abs exercise

1r + 3b = 67

1r + 1b = 29 Since the r's have same coefficient, can just subtract as is.

2b = 38 b = 19 min.

r = 29 - b; r = 10 min.

Answer 2

Let x = the number of minutes of 1 arm routine and y = the number of minutes of

1 abdominal routine, so then we can transform the above information into

a system of 2 equations and 2 unknowns and then solve it like this:

"a total of 67 minutes by doing 1 arm routine and 3 abdominal routines"

turns into (1) 67 = 1x + 3y, and

"1 arm routine and 1 abdominal routine and spent a total of 29 minutes"

turns into (2) 29 = 1x + 1y.

So, now we can subtract equation 2 from equation 1 to get the following:

67 - 29 = 1x + 3y - 1x - 1y, so we get 38 = 0x + 2y = 2y, so y = 19 minutes,

Then, we can plug y = 19 into the second equation to get the following:

29 = 1x + 1*19, so 29 = 1x + 19, so 29 - 19 = 1x, so x = 10 minutes.

Therefore, we finally have that 1 arm routine takes 10 minutes

and 1 abdominal routine takes 19 minutes.

Answer 3

Let r = the # of mins on arms.

Let b = the # of mins on abs.

r + 3b = 67

r + b = 29

I'm going to solve the both equations for r.

r + 3b - 3b = 67 - 3b

r = 67 - 3b

r + b - b = 29 - b

r = 29 - b

Well, if r = 67 - 3b and r = 29 - b, then...

67 - 3b = 29 - b

The rest is on you. Go!