Question

Li keeps track of the time he spends working out each week. The table shows the

number of cardio workouts and the number of weighted workouts for 3 recent weeks,
The total time in minutes for weeks 1 and 2 are given. Each cardio workout is the same
length of time, and each weighted workout is the same length of time. The system of
equations can be used to represent this situation.
Use the drop-down menus to complete each statement.

Answer 1

The total time Li spent for week 3 was 210 minutes.

Explanation:

Step 1; Assume x to be the number of cardio workouts a week and y be the number of weighted workouts a week, so we have

4x + y = 210, take this as equation 1 ,

3x + 2y = 195, take this as equation 2 .

Step 2; We multiply equation 1 with 2 and equation 2 with 1 so we can cancel out the variable x in both equations. By doing this we get

8x + 2y = 420, take this as equation 3,

-18x +4y =32, this is equation 2

If we subtract equation 2 from equation 3, we cancel out the y variable and can calculate the value of x.

5x = 225 , x = 225/5 = 45, x = 45.

Step 3; Substituting this value of x in any of the previous equations we will get x's value. Here this value of x is substituted in equation 1.

4(45) + y = 210, 180 + y = 210 , y = 210 - 180, y = 30.

So we have x = 45 and y = 30.

Step 4; Now we calculate the time spent in the third week by substituting the values of x and y in 2x + 4y,

2x + 4y = 2 (45) + 4 (30) = 90 + 120 = 210 minutes.