Hi there’s this question that’s been bothering me.The question is Ellie has £3.20 to spend on pens.However each pen is 2p dearer than she expected,so she has to buy 8 fewer than planned.What is the cost of each pen.
I’m really stuck with this question and it would help if you would take me through each step.Thank you so much
MAth quadratics?
2018-01-23 3:38 pm
回答 (2)
2018-01-23 3:58 pm
✔ 最佳答案
Let c pen and n be the cost of each pen and the number of pens he buys.Then, his expects cost for each pen is (c - 2) p, and he expects to buy (n + 8) pens.
cn = 3.20 × 100 …… [1]
(c - 2)(n + 8) = 3.20 × 100 …… [2]
From [1] :
n = 320/c …… [3]
Substitute [3] into [2] :
(c - 2)[(320/c) + 8] = 320
(c - 2)[(320/c) + 8] * c = 320 * c
(c - 2)(320 + 8c) = 320c
8c² + 304 - 640 = 320c
8c² - 16c - 640 = 0
c² - 2c - 80 = 0
(c - 10)(c + 8) = 0
c = 10 or c = -8 (rejected)
The cost of each pen = 10 p
2018-01-23 3:51 pm
Let c represent the cost of the pen. Then 3.20/c is the number of pens Ellie bought. This is 8 fewer than the number she could have bought if the cost were c-0.02. Hence, ...
.. 3.20/(c -.02) -3.20/c = 8
Multiply by the product of the denominators
.. 3.20*(c -(c -.02)) = 8*c*(c -.02)
.. 8c^2 -0.16c -0.064 = 0
.. 8(c -0.10)(c +0.08) = 0
We want the positive solution, so
.. c = 0.10
The cost of each pen is 10p.
_____
Ellie bought 32 pens. Had the price been 8p as planned, she could have bought 40 pens.
.. 3.20/(c -.02) -3.20/c = 8
Multiply by the product of the denominators
.. 3.20*(c -(c -.02)) = 8*c*(c -.02)
.. 8c^2 -0.16c -0.064 = 0
.. 8(c -0.10)(c +0.08) = 0
We want the positive solution, so
.. c = 0.10
The cost of each pen is 10p.
_____
Ellie bought 32 pens. Had the price been 8p as planned, she could have bought 40 pens.
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