<PRE><B>Question 1108917</B>
let x = number of dresses and y = number of shoes.


the cost of each dress is 400 dollars and the cost of each pair of shoes is 1000 dollars.


the total cost is 48,000.


therefore:


400x + 1000y = 48,000.


that equation says that the number of dresses * 400 plus the number of pairs of shoes * 1000 equals the total cost of 48000.


the total profit is 18000.


the profit margin on dresses is 20%.
the profit margin on shoes is 50%.


the profit on the dresses is 20% of the cost of the dresses.


therefore, the profit on the dresses is .20 * 400 * x.


the profit on the shoes is 50% of the cost of the shoes.


therefore, the profit on the shoes is .50 * 1000 * y.


since the total profit is 18,000, you get:


.20 * 400 * x + .50 * 1000 * y = 18,000.


looks like we have 2 equations that need to be solved simultaneously.


they are:


400x + 1000y = 48,000
.20 * 400 * x + .50 * 1000 * y = 18,000


simplify the second equation and leave the first equation as is to get:


400x + 1000y = 48,000
80x + 500y = 18,000


leave the first equation as is and multiply both sides of the second equation by 2 to get:


400x + 1000y = 48,000
160x + 1000y = 36,000


subtract the second equation from the first to get:


240x = 12,000


solve for x to get:


x = 12000 / 240 = 50


you have x = 50


your 2 original equations, after simplification, are:


400x + 1000y = 48,000
80x + 500y = 18,000


replace x with 50 in the first original equation to get:


400*50 + 1000y = 48,000


simplify to get:


20,000 + 1000y = 48,000


solve for y to get y = (48,000 - 20,000) / 1000 = 28.


you have x = 50 and y = 28


replace x with 50 and y with 28 in the second original equation to get:


80x + 500y = 18,000 becomes:


80 * 50  + 500 * 28 = 18,000


simplify to get 4,000 + 14,000 = 18,000.


both original equations are true when x = 50 and y = 28, so that must be your solution.


she bought 50 dresses and 28 pairs of shoes.


the dresses cost her 50 * 400 = 20,000.
the shoes cost her 28 * 1000 = 28,000.


her total cost was 20,000 + 28,000 = 48,000.


she made 20% profit on the dresses.
she made 50% profit on the shows.


her profit on the dresses was .20 * 20,000 = 4,000.
her profit on the shoes was .50 * 28,000 = 14,000.


her total profit was 4,000 + 14,000 = 18,000.


solution checks out and is therefore assumed to be good.


solution is 50 dresses and 28 pairs of shoes were bought.














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