SOLUTION: Please help. SAT Problems: For what values of p does the equation px = 10 have a solution −5; 1; 20? For what values of m does the equation mx = 5 have a single solution?

Question 1148094: Please help.
SAT Problems:
For what values of p does the equation px = 10 have a solution −5; 1; 20?
For what values of m does the equation mx = 5 have a single solution? Can m have a value for which the equation does not have solutions; have infinite number of solutions?
Miriam left Chicago at 9:00 AM and headed to Washington. The first 2 hour Miriam averaged 70 mph. But after she decided to reach Washington at 6:00 PM, she increased her speed. What was her speed after increasing, if the distance between the cities is 700 miles.
I actually tried to solve these problems. Please help(please include the steps too). Thank you! Thank you so much!
Answer by greenestamps(13203) (Show Source): You can put this solution on YOUR website!

For the first two questions, the statements of the problems are not at all clear....

For any equation of the form A*B=C, as long as C is not 0, the equation has a single solution for A given a value for B, and a single solution for B given a value of A.

If in an equation of that form C=0, then one of A or B has to be 0; then there is an infinite number of solutions for the other number, since any number times 0 is 0.

There are no equations of that form that have no solutions.

last question....

The trip is 9 hours, from 9am to 6pm; in the first 2 hours at 70mph, she travels 70*2=140 miles; she has 700-140=560 miles left to go; she wants to travel those 560 miles in 9-2=7 hours.

What speed is required to travel 560 miles in 7 hours?

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