Pre-Cal help?

2017-01-10 1:06 pm

Hi, I'm working on an assignment using substitution/elimination to solve systems of equations. I've asked a previous question asking for help on this same assignment and I just finished four questions but recently stumbled on a few that confused me.

1) A wholesale clothier declined an offer of $4000 for some suits. Later, he sold all but 5 of the suits at an increase price of $10 per suit over the original offer, receiving $4500 for the sale. How many suits did he sell and what was the original offer per suit?

equations I came up with:

4000 = xy
(y - 5) (x + 10) = 4500

2) The path of an underground stream is given by the function y = 4x^2 + 17x - 32. Two new houses need wells to be dug. On the area plan, these houses lie on a line defined by the equation y = -15x + 100. Determine the coordinates where the two new wells should be dug.

回答 (1)

用戶48544

2017-01-10 1:27 pm

✔ 最佳答案

　
1.

OK, again your equations look good, with
x = original offer per suit
y = number of suits

4000 = xy ----> y = 4000/x

Substitute y in 2nd equation with 4000/x, then solve for x:

(y − 5) (x + 10) = 4500
(4000/x − 5) (x + 10) = 4500
x(4000/x − 5) (x + 10) = 4500x
(4000 − 5x) (x + 10) = 4500x
4000x + 40000 − 5x² − 50x = 4500x
−5x² − 550x + 40000 = 0
−5 (x² + 110x − 8000) = 0
−5 (x − 50) (x + 160)
x = 50

y = 4000/50 = 80

Number of suits sold = y−5 = 75
Original offer per suit = $50

2.

This is an oddly worded question.

I can only assume that we are supposed to find the points of intersection of the parabola and the line.

However, it is possible for a house to be located on this line, but for the closest spot on the parabola (underground stream) to not be located at one of the points of intersection.

y = 4x² + 17x − 32
y = −15x + 100

4x² + 17x − 32 = −15x + 100
4x² + 32x − 132 = 0
4 (x² + 8x − 33) = 0
4 (x − 3) (x + 11) = 0
x = 3 or −11

x = 3 ---> y = −15(3) + 100 = 55
x = −11 ---> y = −15(−11) + 100 = 265

Well should be dug at coordinates (3, 55) and (−11, 265)

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