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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..

  • math -

    let's switch your a and b to x and y to make it more obvious for the x-y plane

    x + y ≤ 9 (#1)
    20x + 34y ≤ 240 or
    10x + 17y ≤ 120 (#2)

    consider the "equation" for each

    remember to find the x-intercept you let the y=0 and
    to find the y-intercept 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 y-intercept is (0,12) and the x-intercept 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.

  • math -

    thank you!

  • math -

    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 = 9-5 = 4
    if x = 4, y = 9-4 = 5

  • math -

    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 y-intercept?

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