Algebra 2 !!

Question

It costs a silversmith 80$ to make 100 rings and 200$ to make 500 rings. Assuming a linear relationship and cost is a function of rings, how much does it cost to make 1,500 rings? 

Answer 1

If c is variable cost of 1 ring, and f is the cost fixed setup cost (applies from 1 ring to any no of rings), then:

Total cost for 100 rings: 100c+f=$80

Total cost for 500 rings: 500c+f=$200

Subtracting 500c+f-100c-f=$200-$80 > 400c=$120 > c= $120/400=$0.30 cost/ring

To find fixed setup cost f=$80-100*$0.30= $50

 

Therefore total cost of 1500 rings= 1500c+f= 1500*$0.30+$50 = $500

 

Answer is $500

Answer 2

(200 - 80) / (500 - 100)

120 / 400

12 / 40

6 / 20

3 / 10

 

y = 3x/10 + b

80 = 3(100)/10 + b

80 = 30 + b

50 = b

 

y = 3(1500)/10 + 50

 

How much do 1500 rings cost?