Algebra 1 problems

Question

Please help me with these problems and explain the steps to get to the answer:

 

1. Hearst Castle if 180 miles from Ventura by road. Two coaches leave Ventura at the same time, both heading for Hearst Castle, but one averages 5 mph faster than the other. If the faster coach reaches Hearst Castle half an hour earlier than the slower coach, what is the average speed of the faster coach?

 

2. A cyclist completes a 150-mile race in a certain amount of time. She completes another 150-mile race a month later, but this time it takes an hour longer to cover the same distance and her average speed is 5 mph less than in the first race. Find the average speed for the cyclist during her first race.

 

3. Juan's band produced a number of CDs to sell at a gig. The batch of CDs cost $170.00 to make and each CD was sold for $2.50 more than it cost to produce. Juan gave 2 CDs to his friends, but sold the rest for a total of $198.00. How many CDs did Juan produce?

 

4. Chen bought a bag of groceries weighing 15 pounds. His friend, Jo, bought a bag of groceries that also weighed 15 pounds, but contained one less item. The average weighted per item for Jo's groceries was a 1/2 pound more than for Chen's. How many items were in Jo's grocery bag?

 

5. Jose ordered a box of fruits for his market stand costing $6. When his order arrived, Jose discovered that 20 fruits were rotten and threw them in the trash. He sold all of the remaining fruits for a total of $8, charging 3 cents more for each fruit than he paid for it. How many fruits did Jose order begin with?

 

6. A wholesaler bought a batch of T-shirts for $77.00. She gave  two of the T-shirts to her daughters and then sold the rest for a total of $90. If the wholesaler sold each T-shirt for $2 more than it cost her, how much did she pay for each T-shirt?

Answer 1

faster coach goes 45 miles per hour, going 180 miles in 4 hours

slower coach goes 40 going 180 in 4.5 hours

FT=180=(F-5)(T+1) F=faster coach's speed, T=time of faster coach

T=180/F

(F-5)(180/F +1) = 180

similar equations for the rest of the problems

1st race: 30 mph, 2nd race 25 mph

5 hours for 1st race, 6 hours for 2nd race

20 CDs at $8.50 at cost of $170

18 CDs sold at $11, total $198

Jo has 5 items

Chen has 6

Jo's average weight per item = 15/5 = 3 pounds

Chen's 15/6 = 2.5 lbs. 3 = 1/2 lb + 2.5

120 for 5 cents totals $6

100 for 8 cents total $8

wholesaler paid $5.50 for 14 shirts

then sold 12 for $7.50