(50 POINTS - WILL GIVE BRAINLIEST TO MOST HELPFUL ANSWER) I need help quickly-

Pam likes to practice dancing while preparing for a math tournament. She spends 80 minutes every day practicing dance and math. To help her concentrate better, she dances for 20 minutes longer than she works on math.

Part A: Write a pair of linear equations to show the relationship between the number of minutes Pam practices math every day (x) and the number of minutes she dances every day (y). (5 points)

Part B: How much time does Pam spend practicing math every day? Show your work. (3 points)

Part C: Is it possible for Pam to have spent 60 minutes practicing dance if she practices for a total of exactly 80 minutes and dances for 20 minutes longer than she works on her math? Explain your reasoning. (2 points)

Part A:

x + y = 80

x + 20 = y

Part B:

Pam spends 30 minutes practicing math every day.

Part C:

It is not possible for Pam to have spent 60 minutes practicing dance because this means she must have practiced math for 40 minutes (60 - 20 = 40). This would total out to 100 minutes of total practice, not 80 minutes. Therefore, this is impossible.

Step-by-step explanation:

Part A:

"She spends 80 minutes every day practicing dance and math."

x + y = 80

"She dances for 20 minutes longer than she works on math."

x + 20 = y

Part B:

Solve for x:

x + 20 = y

Isolate variable x:

x = y - 20

Plug in this new value for the first equation:

y - 20 + y = 80

Combine like terms:

2y - 20 = 80

Isolate variable y:

2y = 100

y = 50

Plug in the new value of y into any equation:

x + 50 = 80

Isolate variable x:

x = 30

Part C:

x + 20 = y

x + 20 = 60

x = 40

x + y = 80

40 + 60 = 80

100 = 80

Impossible.

Pam likes to practice dancing while preparing for a math tournament. She spends 80 minutes every day practicing dance and math.To help her concentrate better, she dances for 20 minutes longer than she works on math.

Solution given:

let math be x and dance be y.

She spends 80 minutes every day practicing dance and math.means:

x+y=80[I]

and

she dances for 20 minutes longer than she works on math.means:

y=x+20[2]

Part A: Write a pair of linear equations to show the relationship between the number of minutes Pam practices math every day (x) and the number of minutes she dances every day (y).

Solution given:

solving equation [I]

x+y=80

x=80-y is a linear equation for x(math)

and

y=x+20 is a linear equation for y (dance)

Part B: How much time does Pam spend practicing math every day? Show your work. (3 points)

Substituting value of y in equation [I]

x+(x+20)=80

open bracket

x+x+20=80

subtract both side by 20

2x+20-20=80-20

2x=60

dividing both side by 2

2x/2=60/2

2x/2=60/2x=30min

Part C: Is it possible for Pam to have spent 60 minutes practicing dance if she practices for a total of exactly 80 minutes and dances for 20 minutes longer than she works on her math? Explain your reasoning.

No it is not possible:

y=60

x+20=y[I]

substituting value of y

x=60-20

x=40

now

total =x+y=40+60=100

which is not equal to 80°

(c, 0) i might be wrong so don't put full faith on my answer

answer: e 9, 5.75

step-by-step explanation:

step 1

find the variation ab in the x coordinate

delta x=(x2-x1)=10-> 8 units

find the variation ab  in the y coordinate 

delta y=(y2-y1)=6-> 2 units

step 2

find the coordinates point c

  x coordinate 

cx=ax+delta x*2/> cx=2+8*(2/> cx=3

  y coordinate 

cy=ay+delta y*2/> cy=4+2*(2/> cy=4.25

the coordinates of point c are (3,4.25)

step 3

find the coordinates point d

  x  coordinate 

dx=ax+delta x*4/> dx=2+8*(4/> dx=4

  y  coordinate 

dy=ay+delta y*4/> dy=4+2*(4/> dy=4.5

the coordinates of point d are (4, 4.5)

step 4

find the coordinates point e

  x  coordinate 

ex=ax+delta x*4/> ex=2+8*(6/> ex=5

  y  coordinate 

ey=ay+delta y*4/> ey=4+2*(6/> ey=4.75

the coordinates of point e are (5, 4.75)

step 5

find the coordinates point f

  x  coordinate 

fx=ax+delta x*4/> fx=2+8*(8/> fx=6

  y  coordinate 

fy=ay+delta y*4/> fy=4+2*(8/> fy=5

the coordinates of point f are (6,5)

step 6

find the coordinates point g

  x  coordinate 

gx=ax+delta x*4/> gx=2+8*(10/> gx=7

  y  coordinate 

gy=ay+delta y*4/> gy=4+2*(10/> gy=5.25

the coordinates of point g are (7,5.25)

step 7

find the coordinates point h

  x  coordinate 

hx=ax+delta x*4/> hx=2+8*(12/> hx=8

  y  coordinate 

hy=ay+delta y*4/> hy=4+2*(12/> hy=5.5

the coordinates of point h are (8,5.5)

step 8

find the coordinates point i

  x  coordinate 

ix=ax+delta x*4/> ix=2+8*(14/> ix=9

  y  coordinate 

iy=ay+delta y*4/> iy=4+2*(14/> iy=5.75

the coordinates of point i are (9,5.75)

- r3ktforgood ☕