At the supermarket checkout, the scanner records prices of foods you buy. To protect consumers, state of Michigan passed "scanning law" which says something similar to following: If there is discrepancy between price marked on item and price recorded by scanner, consumer is entitled to get 10 times difference between those prices; this amount given should be at least $1 and at most $5. The consumer will be given difference between prices, additionally to amount calculated above.
For instance: If difference is 5c/, you must receive $1 (as 10 times difference is only 50c/ and you are to receive at least $1), plus difference of 5c/. Therefore, total you must receive is $1.00 + $0.05 = $1.05, If difference is 25c/, you should get 10 times difference additionally to difference, giving(10)(0.25) + 0.25 = $2.75.
If difference is 95c/, you must get $5 (because 10(.95) = $9.50 is more than $5, the maximum penalty), plus 95c/, giving 5 + 0.95 = $5.95.
(a) Find lowest possible refund?
(b) Assume x is difference between price scanned and price marked on item, and y is amount refunded to customer. Write the formula for y in terms of x.
(c) What would difference between price scanned and price marked have to be to get a 9.00 refund?
(d) Graph y as the function of x.