A man sold a chair and a table together for $1520 thereby, making a profit of 25% on chair and 10% on table. By selling them together for $1535 he would make profit of 10% on the chair and 25% on table. Find the cost price.
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To solve this problem, we need to set up a system of equations.
Let's assume the cost price of the chair is Cc and the cost price of the table is Ct.
According to the given information, when the chair and table are sold together for $1520, the man makes a profit of 25% on the chair and 10% on the table. So, we can write the equation:
Cc + Ct + 0.25Cc + 0.1Ct = 1520 --(1)
Similarly, when they are sold together for $1535, the man makes a profit of 10% on the chair and 25% on the table. So, we can write the equation:
Cc + Ct + 0.1Cc + 0.25Ct = 1535 --(2)
Now, we can solve these two equations simultaneously to find the values of Cc and Ct.
Subtracting equation (2) from equation (1), we get:
0.25Cc - 0.1Cc + 0.1Ct - 0.25Ct = 1520 - 1535
0.15Cc - 0.15Ct = -15 --(3)
Simplifying equation (3), we get:
0.15(Cc - Ct) = -15
Cc - Ct = -100 --(4)
Next, let's add equation (2) and equation (4):
Cc + Ct + 0.1Cc + 0.25Ct + Cc - Ct = 1535 - 100
2Cc + 0.1Cc + 0.25Ct - Ct = 1435
2.1Cc - 0.75Ct = 1435 --(5)
Now, we have a system of two equations:
Cc - Ct = -100 --(4)
2.1Cc - 0.75Ct = 1435 --(5)
We can solve this system of equations to find the values of Cc and Ct.
One way to solve this system is by substitution. From equation (4), we can rewrite Cc as Ct - 100 and substitute it into equation (5):
2.1(Ct - 100) - 0.75Ct = 1435
2.1Ct - 210 - 0.75Ct = 1435
1.35Ct = 1645
Ct = 1645 / 1.35
Ct ≈ 1220.37
Now, substitute the value of Ct back into equation (4) to find Cc:
Cc - 1220.37 = -100
Cc ≈ 1120.37
Therefore, the cost price of the chair is approximately $1120.37 and the cost price of the table is approximately $1220.37.