# math

Liam is the founder and president of the Justin Bieber Fan Club. As a fundraiser, the JBFC sells chocolate-flavored spaghetti sauce. The current price is \$6.40 per jar and their average monthly sales are 250 jars. They are considering raising prices and have been surveying customers to determine if this is a good decision. They have determined that every \$0.10 increase in price will cost them 5 sales per month. Determine the range of prices that they could charge in order to make at least \$1500 per month. (I have tried all I can think of but I can't figure out how to solve this. Any help would be very useful. I've put it into the equation 1500=(250-5r) (6.40+0.10r)

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1. Your equation looks good. So, just solve it and you get

(250-5r) (6.40+0.10r) >= 1500
-.5r^2 - .7r + 1600 >= 1500
.5r^2 + .7r - 100 >= 0
Now, solve the left side using the quadratic formula, and you find that

.5r^2 + .7r - 100 = 0 at
x = -22.8 and 8.8

Between those two roots, the function is positive, so since we are dealing with the real world, we need r>=0, and we have

.5r^2 + .7r + 1600 >= 1500
for 0 <= r <= 8

Now you can figure the actual price range.

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posted by Steve
2. I haven't learned how to find a function. Do you mind walking me through it?

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posted by Rachelle
3. Excuse me? You developed your own function. The price after r rate increases is

6.40 + 0.1r

so, for r=0, the price is 6.40
for r=8, the price is 6.40+.1*8 = 7.20

Between those two prices, she'll make at least \$1500.

Take a look at

http://www.wolframalpha.com/input/?i=plot+y%3D%28250-5r%29+%286.40%2B0.10r%29%2C+y%3D1500

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posted by Steve

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