Answer:
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
Pam spends 30 minutes practicing math every day.
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°
So not possible.
