Alice works part-time after school. On Monday Alice records that she worked three and one-fourth hours. On Tuesday Alice records that she works one and three-fourths hours. On Wednesday Alice records that she works two and two-thirds hours. On Friday Alice records that she works for Five and one-half hours. Alice knows that she worked sixteen and one-half hours for five days. Alice forgot to record how many hours she worked on Thursday. How many hours did she work on Thursday? Alice earns seven dollars and fifty cents per hour. Alice needs hundred forty six dollars and twenty five cents to buy a new game player. How many more hours does Alice have to work to have enough money to buy the game player? Show your work.

Check explanation

Step-by-step explanation:

Monday = 3 1/4 hours

Tuesday = 1 3/4 hours

Wednesday = 2 2/3 hours

Thursday = x hours

Friday = 5 1/2 hours

Total hours worked = 16 1/2 hours

Total hours worked = Monday + Tuesday + Wednesday + Thursday + Friday

16 1/2 = 3 1/4 + 1 3/4 + 2 2/3 + x + 5 1/2

33/2 = 13/4 + 7/4 + 8/3 + x + 11/2

33/2 = 39+21+32+66/12 + x

33/2 = 158/12 + x

33/2 - 158/12 = x

x = 198-158/12

x = 40/12

= 3 4/12

x = 3 1/3 hours

Earnings per hour = $7.50

Total earnings = Earnings per hour * Total hours worked

= 7.50 * 16 1/2

= 7.50 * 33/2

= 7.50 * 16.5

= $123.75

Amount needed to purchase a game player = $146.25

Amount needed more =$146.25 - $123.75

= $22.5

More hours needed to work = Amount needed more / Earnings per hour

= $22.5 / $7.50

= 3 hours

Therefore,

Alice needs to work 3 hours more