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# Mathematics Homework (variations)(III)

Mathematics Homework (variations)(III)

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.

Rating

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%