Hime with this!
pam likes to practice dancing while preparing for a math tournament. she spends 80 minutes every day practicing dance and math. to her concentrate better on math, she spends 20 minutes more dancing than doing 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 practices dances every day (y).
part b: how much time does pam spend on practicing math every day?
part c: is it possible for pam to have spent 60 minutes practicing dance every day? explain your reasoning.

Solutions 

We know that 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 on math, she spends 20 minutes more dancing than doing math. 

----------- Calculations 

Part A: Let variable "d" represent = minutes dancing 

Let variable "m" represent= minutes doing math  

We know that she spends 80 mins doing both. 

d + m = 80  

She dances for 20 min more than she does math 

d = m + 20  

Now we have a system of equations 

Part B: Solve for variable m  





 

 
 


Now that we know "m", we can solve for variable "d" 

 

 
 


Pam dances for 50 min and does math for 30.

Part C: You can figure out if she can spend that much time by plugging in the value of 60 in for the variable d.

    Plug in 60 for y

         Subtract 60 from both sides



Plug in both values to find second equation.

     Plug in both values

 

20 ≠ 80

20 does not equal 80, so no, she cannot spend 60 minutes dancing each day. For variable "d" to equal 80 then she would have to do math for 40 minutes.