How long was the workweek in the old contract

Question

A new labor contract provides for a wage increase of $1 per hour and a reduction of 5 hours in the workweek. A worker who received $245 per week under the old contract will receive $240 per week under the new contract. How long was the workweek under the old contract?

Answer 1

p = pay in $/hour

h = # hours worked

 

ph = 245 {equation 1}

p = 245/h

 

(p+1)(h-5) = 240  {equation 2}

ph - 5p + h - 5 = 240

245 - 5p + h = 245

h - 5p = 0

 

h - 5(245/h) = 0

h - 1225/h = 0

h² - 1225 = 0

h² = 1225

h = √1225

h = 35

 

Under the old contract employees worked 35 hrs/week

 

check:  p = 245/h = $7 per hour originally

 

new salary: (p+1)(h-5) = 240

(7+1)(35-5) = 240

8(30) = 240

240 = 240

This checks correct.