Please see the attached file (boxes) for answers.

52. How can a graph be used to determine how many solutions an equation has?

Plot y against x. The values of x at which the plot cuts the x axis are the solutions. The number of points at which the x axis is crossed is the number of solutions.

8. Bobbi picks 1 qt in 20 minutes. Blanche picks 1 qt in 25 minutes. How long would it take them to pick one quart if they work together?

Let the rate at which Bobbi works = x qt/min
Let the rate at which Blanche works = y qt/min
Combined rate = x + y qt/min
Time taken to pick 1 qt = 1 qt / (x+y) qt/min = 1/ (1/20+ 1/25) = 1/ {(5+4)/ 100}
= 100/9 minutes = 11 1/9 minutes

14. The speed of a freight train is 15 mph slower than the speed of a passenger train. The freight train travels 390 miles in the same time that it takes the passenger train to travel 480 miles. Find the speed of each train.

F = speed of the freight train in miles/hr, and P = speed of the passenger train in miles/hr:
F = P - 15 miles/ hr
Time taken to cover 390 miles for freight train = 390 miles / F miles/hr = 390 /F hr
Time taken to cover 480 miles for passenger train = 480 miles / P miles/hr = 480 /P hr
According to the conditions in the problem
390/F hr = 480/P hr
Combining the equations and solving for P:

(P - 15) = P
390 480

480(P - 15) = 390(P)

480P - 7200 = 390P

90P -7200 = 0

90P = 7200

P = 80

Since, F = P - 15, then F = 65

Therefore, speed of Freight train = F miles/hr = 65 miles/hr
Speed of Passenger train = P miles/hr = 80 miles/hr

44. It takes 60 oz. of grass seed to seed 3000 ft ^2 of lawn. At this rate, how much would be needed to seed 5000 ft^2 of lawn?

Amount of grass seed required to seed 3000 ft 2 of lawn = 60 oz
Therefore, amount of grass seed required to seed 1 ft 2 of lawn
= 60 oz ( 1 ft 2 / 3000 ft 2 ) = 60 / 3000 oz = (1/ 50) oz
Amount of grass seed required to seed 5000 ft 2 of lawn = 5000 (1/50) oz = 100 oz

Alternatively;
Let x oz be the amount required to seed 5000 ft 2 of lawn

60 oz = x oz
3000 ft 2 5000 ft 2
Cross-multiplying and solving for x:

60(5000) = 3000x

Or x = 100
Therefore, amount of seed required = x oz = 100 oz