Question 1108917: If Joshua paid for 48,000$ for all of his expenses, consiting of dresses and shoes, with each dress being 400$ and each pair of shoes being 1000$, after he sold all of then he had a profit of 18,000$ with a profit of 20% for the dresses, and profit of 50% for the shoes, how many shoes and dresses did Joshua buy?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! 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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