SOLUTION: Well I didn't know which kind of problem it was so I'm wondering if you could help me with a couple questions: If flour comes in 2 pound bags and in 5 pound bags, list all the way

Question 167434: Well I didn't know which kind of problem it was so I'm wondering if you could help me with a couple questions:
If flour comes in 2 pound bags and in 5 pound bags, list all the ways to buy exactly 18 pounds of flour. Draw a graph and loacte the solutions on teh graph. What can you say about the solutions that appear on the graph?
NEXT QUESTION:
Ms. O'Brien has written a math exam with two parts. Part I has 9 questions , and part II has 8 questoins. She wants to know how to assign points to each part so that the total will be exactly 100 points. Find a Diophantine equation that represents this situation and solves Ms. O'Brien's problem.
Make a table to represent tests that ahve 9 qeustions in part I, 8 questions in part II and 200 points in all.

LAST QUESTION:
How can you tell that 4x + 6x = 125 has now whole-number solution?
How can you tell that 5x + 10y = 112
How can you tell whether 6s + 9y = 100 has whole-number solutions?
Answer by vleith(2825) (Show Source):
You can put this solution on YOUR website!
Graph the line and then find the points on the graph that intersect the integer grid. You'll the only two points that fall on integers grid is (9,0) and (4,2)

Use
4x + 6y=125 can;t happen since no combination of even numbers can add to an odd result
5x+10y must end in either 5 or 0. No way to get to 112
Last one:
1)Graph and see if there are points on the grid (assumes grid is on integers)
2)Plug and try (100,91,82,73,64,55,46,37,28,19,10,1) Any any of those evenly divisible by 6? I dont think so