Assumption / supposition method :


① Assume first that all 1000 casings were in good condition, none are scratched.

Under this assumption, amount that Yvonne has to pay for them

= $0.50 × 1000
= $500

② Since the actual amount that Yvonne paid was $300, the assumption resulted in an over-projection of the cost.

Difference between assumed cost and actual cost = $500 - $300 = $200


③ The assumption is not correct, the number of casings in good condition have to reduced, and those scratched have to be increased in number

(such that the total number of casings is still 1000)

④ For every 1 good casing reduced, $0.50 has to be taken away from the amount paid by Yvonne.

(Treat it like giving the money back to her)


And, when we replace that casing by adding one scratched casing, $4.50 has to be subtracted as well since the company has to refund Yvonne.

(This is as good as saying that Yvonne gets back another $4.50)


Total reduction in cost for every 1 reduction of good casing/addition of scratched casing

= $4.50 + $0.50
= $5.00


⑤ Since the cost has to be reduced by $200,

Number of good casings to be reduced
= $200 ÷ $5
= 40


Actual number of good casings sold = 1000 - 40 = 960

Check :

Amount that Yvonne pays for 960 good casings

= 960 × $0.50
= $480

Amount that the company has to refund Yvonne for 40 scratched casings

= $4.50 × 40
= $180


Overall amount that Yvonne oays to the company

= $480 - $180
= $380