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香港早晨 asked in 科學及數學數學 · 1 decade ago

Mathematics Homework (variations)(III)

Mathematics Homework (variations)(III)

Please answer with full step.

1. Mr.Chan is planning to make key rings as souvenirs for his customers. The cost if making a key ring is partly constant and partly varies inversely as the total number of key rings made. When 200 key rings are made, the cost per key ring is $7. When 400 key rings are made, the cost per key rings is $5.

(a) How many key rings should be made if the average cost of a key ring is $6.2?

(b) Find the total cost of making 500 key rings.

(c) If the cost of the constant part is increased by 10%, find the percentage change of the total cost of making 500 key rings.

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  • 1 decade ago
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    1. Mr.Chan is planning to make key rings as souvenirs for his customers. The cost if making a key ring is partly constant and partly varies inversely as the total number of key rings made. When 200 key rings are made, the cost per key ring is $7. When 400 key rings are made, the cost per key rings is $5.

    (a) How many key rings should be made if the average cost of a key ring is $6.2?

    C = cost of making a key ring

    N = total number of key rings made

    C = A + B/N, A and B are constants

    7 = A + B/200 ---- (1)

    5 = A + B/400 ---- (2)

    (1) - (2), 2 = B/200 - B/400

    B = 800

    7 = A + 800/200

    A = 3

    C = 3 + 800/N

    6.2 = 3 + 800/N

    N = 250

    (b) Find the total cost of making 500 key rings.

    total cost = (500)(3 + 800/500) = 2300

    (c) If the cost of the constant part is increased by 10%, find the percentage change of the total cost of making 500 key rings

    new total cost = (500)[(3)(1.1) + 800/500] = 2450

    (2450 - 2300)/2300*100% = 6.52%

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