The soccer team won their game! Ben spent equal amounts of time in the game passing, shooting, and running. He played for 40 minutes. Madden spent twice as much time running, and three times as much time shooting and passing, as Ben did. He played for 90 minutes. Quinn spent the same amount of time passing and shooting as Ben but ran twice as much. He played for 70 minutes. Which system of equations matches their soccer success? x + 2y + z = 40 2x + 3y + 3z = 90 x + y + 2z = 70 x + y + z = 40 2x + 2y + 3z = 90 x + y + 2z = 70 x + y + z = 40 2x + 3y + 3z = 90 x + 2y + 2z = 70 x + y + z = 40 2x + 3y + 3z = 90 x + y + 2z = 70

x+y+z =40, 2x+3y+3z=90, 2x +y+z=70, you answer totally depends on how you define variable x, y and z. In my solution I choose x, y and z as mentioned in the explanation

Step-by-step explanation:

Lets Assume

x= running time

y= shooting time

z= passing time

For Ben:

As ben spent equal amount of time on all passing, running and shooting, So

x+y+z and he spent total of 40 minutes, it means we got x + y+ z=40

Similarly for Madden

As Madden spent twice as much time running than Ben so we have 2 times running which is 2x and he spent thrice as much time In shooting 3y and passing 3z, and ge spent total of 90 minutes, so we get

2x+3y+3z=90

Finally for Quinn,

As Quinn spent same amount of time on passing and shooting as Ben did, it means we have y+z but he ran twice as much than Ben and he spent total of 70 minutes, the final result is 2x +y+z=70

To make the options clear, the question is:

The soccer team won their game! Ben spent equal amounts of time in the game passing, shooting, and running. He played for 40 minutes. Madden spent twice as much time running, and three times as much time shooting and passing, as Ben did. He played for 90 minutes. Quinn spent the same amount of time passing and shooting as Ben but ran twice as much. He played for 70 minutes. Which system of equations matches their soccer success?

x + 2y + z = 40

2x + 3y + 3z = 90

x + y + 2z = 70

x + y + z = 40

2x + 2y + 3z = 90

x + y + 2z = 70

x + y + z = 40

2x + 3y + 3z = 90

x + 2y + 2z = 70

x + y + z = 40

2x + 3y + 3z = 90

x + y + 2z = 70

x + y + z = 40

3x + 3y + 2z = 90

x + y + 2z = 70

And this is not in the options.

Step-by-step explanation:

We have that:

Ben spent equal amounts of time in the game passing, shooting, and running. Let us assume time variables x, y, and z, for passing, shooting, and running respectively.

The statements above then means

x = y = z.

Because he played for 40 minutes, the minutes he spent passing, shooting, and running sums to 40.

So,

x + y + z = 40(1)

Madden spent twice as much time running as Ben, that will be 2 × z, and three times as much time shooting and passing, that is 3 × y, 3 × x.

He played for 90, all the minutes he spent playing adds up to 90

So,

3x + 3y + 2z = 90(2)

Quinn spent the same amount of time passing x, and shooting y as Ben but ran twice (2 × z) as much. He played for 70 minutes.

So,

x + y + 2z = 70 (3)

(1), (2), and (3) together are the required system of equations.