Question

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! :)

Answer 1

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