A. Jasmine buys a necklace for $100 and wants to earn at least $40 on it but does not want to mark price by more than $80. In this case $40 is 40% {(40:100)·100%} and $80 is 80% {(80:100)·100%}. Then the range of the percent that Jasmine can mark up necklace is [40%,80%].
She also buys a pair of earrings for $130 and wants to earn at least $40 on it but does not want to mark price by more than $80. In this case $40 is nearly 31% {(40:130)·100%} and $80 is 62% {(80:130)·100%}. Then the range of the percent that Jasmine can mark up necklace is [31%,62%].
At last, she buys a ring for $160 and wants to earn at least $40 on it but does not want to mark price by more than $80. In this case $40 is nearly 25% {(40:160)·100%} and $80 is 50% {(80:160)·100%}. Then the range of the percent that Jasmine can mark up necklace is [25%,80%].
B. She should use the maximal number from the left end and the minimum number from the right end, so she should use percent from the range [40%, 50%]. If she wants to maximize her profit, she should select 50%.
C. If she mark up any price by 50%, then the price of a necklace will become $150 {(150%:100%)·100}, the price of a pair of earrings will become $195 {(150%:100%)·130} and the price of a ring will be $240 {(150%:100%)·160}.
D. She pays in total $100+$130+$160=$390. After selling these jewerlies she gets $150+$195+$240=$585. The difference is $585-$390=$195 - her total profit.
