Word Problem: purchasing in-store or thru catalog

[mcheytan]

The problem is as follows:

Ellen ca purchase a computer at store paying the price P and paying for taxes 6% of the price P. She can also purchase it from a catalog paying the price of Q. Will it cost her to purchase the same computer from the store at cheaper price than from the catalog. We have to decide whether the two pieces of information given (when used together) will provide us with exact answer YES or NO.

1)Q-P<50
2)Q=1150$

Well, if we use the first given equation with Q=1150 we have that P>1100,
because 1150-P<50, because P is negative, we turn the < into > and P>1100
Therefore the answer is YES, she will pay more in the store than from the catalog. 6% TAXES will be adding 66 dollars to the P (but P will be bigger than 1100, therefore the tax will be more in reality), therefore 1166>1150.
IS IT THAT SIMPLE???

 

[tkhunny]

That simple? Pretty much. You can talk around it a little more to make it sound more interesting.

Think about "indifference". What price would make sweet Ellen indifferent about the purchase?

Starting with #2 seems easier.

If Q = $1150, then P + 0.06P = P(1.06) = $1,150 ==> $1,084.91 = P would make her indifferent.

$1,084.91 + 0.06*$1,084.91 = 1.06*$1,084.91 = $1,150 -- The total cost is the same.

This leaves us wondering about P. Is it greater than $1,084.91? If so, go with Q. Since we know hint #1, if Q - P < 50, we have P > Q - $50 = $1,100, which clearly is greater than $1,084.91. We were indifferent at P = $1,084.91. We are NOT indifferent at P > $1,100. Go with Q = $1,150.