A club is selling hats and jackets as a fundraiser. Their budget is $1500 and they want to order at least 250 items. They must buy at least as many hats as they buy jackets. Each hat costs $5 and each jacket costs $8. Write a system of inequalities to represent the situation.
Okay I don't know how to set up this problem so if you could, could you go over it step by step? Thanks!
Okay I don't know how to set up this problem so if you could, could you go over it step by step? Thanks!
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x+y=250
5x+8y=1500
substitute
5x+8y=1500
substitute
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let x = # of hats
let y = # of jackets
Parameters:
x + y >_ 250 (at least (greater than or equal to) 250 items in total)
Rearranged (by subtracting x from each side. It's implied that m = -1):
y >_ - x + 250
x >_ y (at least (greater than or equal to) as many hats as jackets)
Rearranged (just reverse the order it's written in now. It's implied that m = 1, b = 0):
y >_ x
5x + 8y <_1500 (5$ per hat, plus 8$ per jacket, for a total of 1500$ or less (lesser than or equal to))
Rearranged (by subtracting 5x from each side, then dividing the whole thing by 8)
y <_ - (5/8)x + (375/2)
let y = # of jackets
Parameters:
x + y >_ 250 (at least (greater than or equal to) 250 items in total)
Rearranged (by subtracting x from each side. It's implied that m = -1):
y >_ - x + 250
x >_ y (at least (greater than or equal to) as many hats as jackets)
Rearranged (just reverse the order it's written in now. It's implied that m = 1, b = 0):
y >_ x
5x + 8y <_1500 (5$ per hat, plus 8$ per jacket, for a total of 1500$ or less (lesser than or equal to))
Rearranged (by subtracting 5x from each side, then dividing the whole thing by 8)
y <_ - (5/8)x + (375/2)