Expert: Josh - 2/19/2004

Question
i have problems on percent.

1) the regular price of a pair of boots is $85. the store marks the boots 25% off. in addition, they print a coupon in the newspaper for an additional 10% off the sale price. bernice thinks the final sale price will be $55.25. michelle thinks the final sale price will be $57.38. who's correct? show the math used to obtain the answer.
2) the wholesale price of a pair of jeans is $24. the wholesale price is the amount the store pays for an item, the retail price is the amount the store charges the customer for an item.

a) to determine the retail price, a 65% mark-up is added to the whole sale price. find the retail price.
b) if the store puts the jeans on sale 65% off the retail price, will the sale price be more, less, or equal to the original wholesale price?

provide explanations as well.

Answer
Okay Amy,

Let the regular price be R, R=85.

With the 25% discount off R,
the discounted sales price, S=R*(1-0.25)=R*0.75. ...[#1]

With a further 10% discount off the sales price,
the final cost is C=S*(1-0.1)=S*0.9 ...[#2]

Using back subsitution, since R=85,
S=85*0.75. ...[from #1]
C=S*0.9=85*0.75*0.9 ...[from #2]

You can verify which is the right answer, using your calculator.

2a) Calculate the mark-up,M.
M=24*0.65
Adding the mark-up (M) to the wholesale price (W=24) gives you the retail price, R.

R=W+M
=24+24*0.65
=24*(1.65) ---use your calculator.

2b) just calculate 24*(1.65)*(1-0.65) and see for yourself.
Actually, W*(1-0.65)(0.65)=W*(0.35*0.65)
and (0.35*0.65) is less than 1, so the end result must be much smaller than W, the wholesale price.