8th grade math

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i have two problems that i need to write an inequality for.

a) One third of a number, decreased by thirty six, is at most twenty two. Find the number.

b) A school's Spanish club is welling bumper stickers. They bought 100 for $55, and have to give 15 cents for every sticker sold. If they plan to sell each sticker for $1.25, how many do they have to sell to make a profit?

Please help and explain so i can understand. Thank you! :)

  • 8th grade math -

    number = n
    one third of number is: n/3
    decreased by 36 is: n/3 - 36
    is at most 22: n/3 - 36 <= 22

    so,

    n/3 - 36 <= 22
    n/3 <= 58
    n <= 174
    --------------------
    cost for n tickets: 55 + .15n
    revenue: 1.25n

    profit is when revenue > cost:
    1.25n > 55 + .15n
    1.1n > 55
    n > 50

    check:
    cost for 50 = 55 + 7.50 = 62.50
    revenue for 50 = 1.25 * 50 = 62.50

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