Melvin plays tennis and swims for a total of 110 minutes every day. He plays tennis 40 minutes more than he swims.

Part A: Write a pair of linear equations to show the relationship between the number of minutes Melvin plays tennis (x) and the number of minutes he swims (y) every day. (5 points)

Part B: How much time does Melvin spend swimming every day? (3 points)

Part C: Is it possible for Melvin to have spent 70 minutes playing tennis every day? Explain your reasoning. (2 points)

A . x = y + 40, where x is time playing tennis in minutes and y is time spent swimming in minutes.

B. Melvin spends 35 minutes of swimming every day.

C. No, Melvin can't spend 70 minutes a day playing tennis.

Step-by-step explanation:

Step 1; It is given that Melvin does both for a total time of 110 minutes. x is the time spent playing tennis and y is the time spent swimming. So

x + y = 110 minutes, take this as equation 1.

It is given that Melvin spends 40 minutes more on tennis than swimming so

x = y + 40, take this as equation 2

Substituting equation 2 in 1, we get,

y + 40 + y = 110,

2y + 40 = 110,

2y = 110 - 40 = 70

y =35

Substitute y = 35 in equation 1

x + 35 = 110,

x = 75.

Step 2; So Melvin spends 35 minutes a day swimming and 75 minutes playing tennis equalling a total of 110 minutes a day.

Step 3; If Melvin spends 70 minutes playing tennis, then he spends 70 - 40 minutes swimming which equals his spending 30 minutes that day swimming. So he spent a total of 70 + 30 minutes that day. So he would have spent 100 minutes that day instead of 110 minutes a day so it wouldn't be possible.

there are many solutions.

step-by-step explanation:

step 1: simplify both sides of the equation.

4x+6=4x^2+10x−4

step 2: subtract 4x^2+10x-4 from both sides.

4x+6−(4x^2+10x−4)=4x^2+10x−4−(4x^2+10x−4)

−4x^2−6x+10=0

step 3: factor left side of equation.

−2(2x+5)(x−1)=0

step 4: set factors equal to 0.

x=-5/2 or x=1