x = cost of car a
y = cost of car b

0.1x - 0.1y = 0.05(x+y) = 1000
2x - 2y = x+y = 20,000
2x - x = y + 2y
x = 3y

from above x + y = 20,000
3y + y = 20,000
y = 5000

x = 20,000 - 5000 = 15000

Therefore cost of both ranges from $5000 - $15000

topspin360 wrote:what's a methodological way of solving this problem that can be generalized and applied to other problems. solution showed plugging in numbers.

A car dealership sold two cars: the first car at a 10% profit and the second car at a 10% loss, which gave them an overall profit of 5% from these two sales. If the dealership's total profit was $1000, what was the cost price of each car?

$5,000 and $1,000
$9,000 and $5,000
$11,000 and $9,000
$15,000 and $5,000
$20,000 and $10,000

Thanks.

This is a MIXTURE problem: a 10% profit and a 10% loss are being combined to form a MIXTURE with a 5% overall profit.
The following approach is called alligation.
It's a very good way to handle MIXTURE PROBLEMS.

Let F = the first car and S = the second car.

Step 1: Plot the 3 percentages on a number line, with the two starting percentages (+10% and -10%) on the ends and the goal percentage (+5%) in the middle.
F(10%)--------------------(+5%)--------S(-10%)

Step 2: Calculate the distances between the percentages.
F(10%)----------5---------(+5)----15----S(-10%)

Step 3: Determine the ratio in the mixture.
The ratio of F to S in the mixture is the RECIPROCAL of the distances in red.
F : S = 15 : 5 = 3:1.

Only answer choice D has the same ratio:
15000:5000 = 3:1.

The correct answer is D.

For two other problems that I solved with alligation, check here:

https://www.beatthegmat.com/ratios-fract ... tml#484583

thanks CEO, the method works perfectly.

Mitch, your method works like a charm! thanks for sharing and pointing to additional problems.

Mitch, quick question of you see this post again.

I understand how to do the following problem (substituting equations) but is there a way to set it up using alligation?

Thanks.

A kilogram of nut mixture contains X% chestnuts and Y% walnuts and sells for $7.00/kg. If the ratio of chestnuts is increased by 50% so that the new mixture is sold for $8.00/kg, what is the price of a kg of walnuts?
1.00 USD
2.50 USD
5.00 USD
7.50 USD
10.00 USD