Fernando 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 88 minutes by doing 2 arm routines and 3 abdominal routines. This week, he has completed 4 arm routines and 1 abdominal routine and spent a total of 66 minutes exercising. How long does each routine last?

Arm routine = 11 minutes

Abdominal routine = 22 minutes

Step-by-step explanation:

Let the minutes used for an arm routine be represented by x.

Let the minutes used for an abdominal routine be represented by y.

Last week, he worked out for a total of 88 minutes by doing 2 arm routines and 3 abdominal routines. This can be expressed as:

2x + 3y = 88

This week, he has completed 4 arm routines and 1 abdominal routine and spent a total of 66 minutes exercising. This can be expressed as:

4x + y = 66

2x + 3y = 88 i

4x + y = 66 ii

Multiply equation I by 4

Multiply equation ii by 2

8x + 12y = 352 iii

8x + 2y = 132 iv

Subtract iv from iii

10y = 220

y = 220 / 10

y = 22

An abdominal routine last for 22 minutes

From equation I

2x + 3y = 88

2x + 3(22) = 88

2x + 66 = 88

2x = 88 - 66

2x = 22

x = 22/2

x = 11 minutes

An arm routine last for 11 minutes