SOS word problem help

Question

Four friends have pre paid cell phones. To determine the number of minutes Warren has left on his phone, add 20 to the number of minutes nancy has and divide the sum by 4. to determine the number of minutes christen has on her phone, multiply the number of minutes nancy has by 3, subtract 50, and then divide by the difference of 2. to determine the number of minutes megan has left on her phone, subtract 20 from the number of minutes nancy has, multiply the difference by 5, and then divide that quantity by 4. how many minutes does each person have left on their phone if they have a total of 195 minutes of time left?

Answer 1

Let N = # minutes Nancy has

     W = # minutes Warren has

     C = # minutes Christen has

     M = # minutes Megan has

 

W = (N+20)/4         20 more than Nancy, divided by 4

C = (3N-50)/2         3 times Nancy, - 50, total divided by 2

M = (5(N-20))/4      5 times the difference of Nancy and 20, quantity divided by 4

 

N + W + C + M = 195    total minutes for all 4 is 195

 

Replace each variable W, C, M with the equivalent expression

 

N + (N+20)/4 + (3N-50)/2 + (5(N-20))/4 = 195

 

To get rid of the fraction multiply everything through by 4

 

4N + (N+20) + 2(3N-50) + 5(N-20) = 4(195)

4N + N + 20 + 6N - 100 + 5N - 100 = 780

16N -180 = 780

16N - 960

N = 960/16 = 60 mins

 

W = (N+20)/4 = 80/4 = 20 mins

 

C = (3N-50)/2 = 130/2 = 65 mins

 

M = 5(N-20)/4 = 200/4 = 50 mins

 

Nancy has 60 mins

Warren has 20 mins

Christen has 65 mins

Megan has 50 mins

 

Total:  195 mins