F.4 Quadratic Equations

2007-10-25 6:02 am

1.If the speed of a car increased by 15km/h in a journary of 240km , 80 minutes would have been saved. Find the original speed of the car.

2.A man bought some photo frames for $540 but 2 were borken. He sold each of the remaining photo frames at $6 more than the cost. Finally, he gained a profit of 10%. How many photo frames did he buy ?

回答 (1)

abaform

2007-10-25 6:36 am

✔ 最佳答案

1.
Let the original speed be x km/h.
240 / (x + 15) = 240 / x - 80/60
240 / (x + 15) = (720 - 4x) / (3x)
(720 - 4x)(x + 15) = 240 * 3x
720x + 10800 - 4x^2 - 60x = 720x
x^2 + 15x - 2700 = 0
(x - 45)(x + 60) = 0
x = 45 or x = -60 (rejected)
The original speed is 45 km/h.
Check:
Original time required = 240 / 45 * 60 = 320 min
New time required = 240 / (45 + 15) * 60 = 240 min

2.
Let n be the number of photo frames he bought, cost of each photo frame = 540/n
(n - 2)(540/n + 6) = 540 * (1 + 10%) = 594
540 + 6n - 1080/n - 12 = 594
6n - 1080/n = 66
n - 180/n - 11 = 0
n^3 - 180n - 11n^2 = 0
n(n^2 - 11n - 180) = 0
n(n - 20)(n + 9) = 0
n = 0 (rejected) or n = 20 or n = -9 (rejected)
He bought 20 photo frames.

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