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# 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.

### 1 Answer

- 雞尾包Lv 71 decade agoFavorite Answer
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%