math
posted by Angie on .
Suppose you need $2.40 in postage to mail a package to a friend. You have 9 stamps, some $0.20 and some $0.34. How many of each do you need to mail the package?
So to solve this problem, I came up with two inequalities:
1. a + b is less than or equal to 9
2. 20a + 34b is greater than or equal to 240
Now I'm supposed to graph both inequalities, but how? I don't know how to find the intercepts for the inequalities or even which interecepts I'm supposed to find..

let's switch your a and b to x and y to make it more obvious for the xy plane
x + y ≤ 9 (#1)
20x + 34y ≤ 240 or
10x + 17y ≤ 120 (#2)
consider the "equation" for each
remember to find the xintercept you let the y=0 and
to find the yintercept you let x=0
so for #1, the x and y intercepts are both 9, so... easy to graph
do the same for 10x + 17y = 120
the yintercept is (0,12) and the xintercept is (appr.7, 0)
now shade in the region which falls below the first line AND the second line in the first quadrant.
Notice they intersect at a point, call that point P
solve the two "equations" to find P.
I used substitution and found x = 33/7
but x is the number of 20 cent stamps, and must be a whole number.
so we have to go either to the next higher x or the next lower x
if x = 5 then y = 9
if x = 4, y = 9
test: if x=5, y=4, cost = 20(5)+34(4)= 236 , not enough
if x=4, y = 5, cost = 20(4) + 5(34) = 250 , which is more than what is needed but is the best we can do. 
thank you!

two of my statements were not complete
in <<if x = 5 then y = 9
if x = 4, y = 9 >>
it should have said:
if x = 5 then y = 95 = 4
if x = 4, y = 94 = 5 
by the way, which way do you think is easier: Finding the intercepts(like above), or rearranging the inequality and graph it by knowing the slope and yintercept?