A trader bought 30 baskets of
potatoes and 100 baskets of oranges
for $2450. She sold the potatoes at a
profit of 40% and the oranges at a
profit of 30%. If her profit on the
entire transaction was $855, calculate the:
1) Cost price for a basket of potato;
2) Selling price of the 100 baskets of
oranges.
If the prices of baskets were x and y, then we are told:
30x+100y = 2450
30*.40x + 100*.30y = 855
so,
potatoes cost $40.00
oranges cost $12.50
wrong
ok - maybe you can catch my mistake, and answer the 2nd part while you're at it ...
pls help me i'm so confuse with the second part.
once you have the price for the oranges (let's say, oh, $12.50), then the total selling price for 100 baskets at 30% markup is
$12.50 * 1.30 * 100 = $1625.00
thank you very much steve!
To solve this problem, we need to set up a system of equations based on the given information.
Let's assume the cost price of a basket of potatoes is 'x' dollars. Therefore, the cost price of 30 baskets of potatoes would be 30x dollars.
Since the trader sold the potatoes at a profit of 40%, the selling price of 30 baskets of potatoes would be (1 + 0.40) times the cost price, or 1.40x.
Similarly, let's assume the cost price of a basket of oranges is 'y' dollars. The cost price of 100 baskets of oranges will be 100y dollars.
Since the trader sold the oranges at a profit of 30%, the selling price of 100 baskets of oranges would be (1 + 0.30) times the cost price, or 1.30y.
Now, we can set up the equations:
1) 30x + 100y = 2450 (total cost price of potatoes and oranges)
2) 30x*0.40 + 100y*0.30 = 855 (profit on the entire transaction)
To solve this system of equations, we can use substitution or elimination method.
Let's solve it using the substitution method:
From equation 1, we can express y in terms of x:
y = (2450 - 30x) / 100
Now, substitute this value of y in equation 2:
30x*0.40 + 100 * ((2450 - 30x) / 100) * 0.30 = 855
Now, simplify and solve for x:
12x + (2450 - 30x) * 0.30 = 855
12x + 735 - 0.9x = 855
11.1x = 120
x = 120 / 11.1
x ≈ 10.81
Therefore, the cost price for a basket of potatoes is approximately $10.81.
To find the selling price of 100 baskets of oranges, substitute the value of x in equation 1:
30 * 10.81 + 100y = 2450
324.3 + 100y = 2450
100y = 2450 - 324.3
100y = 2125.7
y = 2125.7 / 100
y ≈ 21.26
Therefore, the selling price of 100 baskets of oranges is approximately $21.26 per basket.