A man invested 25,000 pesos in two parts; one part was invested at 5% and the other at 7%, how much was invested at 7% if the income from both is 1,410 pesos?
0.07x + 0.05(25000-x) = 1410
Well, well, well, it seems like we have a curious case of financial acrobatics! Let's crack this one open, shall we?
Let's say the amount invested at 5% is x pesos. According to the information provided, the amount invested at 7% would then be 25,000 - x pesos.
Now, let's calculate the income from each amount. The income from the amount invested at 5% would be 0.05x pesos, and the income from the amount invested at 7% would be 0.07(25,000 - x) pesos.
Since the total income is given as 1,410 pesos, we can set up an equation:
0.05x + 0.07(25,000 - x) = 1,410.
Now, we just need to do a little math magic to solve for x.
0.05x + 0.07(25,000 - x) = 1,410
0.05x + 1,750 - 0.07x = 1,410
-0.02x + 1,750 = 1,410
-0.02x = -340
x = -340 / -0.02
x = 17,000.
So, our clownish conclusion is that 17,000 pesos were invested at 5%, and the remaining amount of 25,000 - 17,000 = 8,000 pesos were invested at 7%.
Ta-da! The mystery is solved!
Let's assume the amount invested at 5% is x pesos.
Since the total investment is 25,000 pesos, the amount invested at 7% can be calculated as (25,000 - x) pesos.
The income generated from the 5% investment can be calculated using the formula: x * 0.05.
The income generated from the 7% investment can be calculated using the formula: (25,000 - x) * 0.07.
According to the given information, the total income from both investments is 1,410 pesos.
So, we can set up an equation: x * 0.05 + (25,000 - x) * 0.07 = 1,410.
Let's solve this equation step by step:
0.05x + 0.07(25,000 - x) = 1,410
0.05x + 1,750 - 0.07x = 1,410
-0.02x + 1,750 = 1,410
-0.02x = 1,410 - 1,750
-0.02x = -340
Now, let's divide both sides by -0.02:
x = -340 / -0.02
x = 17,000
Therefore, the man has invested 17,000 pesos at 5% and (25,000 - 17,000) = 8,000 pesos at 7%.
To solve this problem, we can use a system of equations. Let's denote the amount invested at 5% as x pesos, and the amount invested at 7% as y pesos.
According to the problem, the total amount invested is 25,000 pesos, so we have the equation:
x + y = 25,000 ---- (equation 1)
The income from the investment at 5% can be calculated using the formula:
Income from 5% investment = (Amount invested at 5% * Interest rate of 5%) = (x * 5/100) = 0.05x
Similarly, the income from the investment at 7% can be calculated using the formula:
Income from 7% investment = (Amount invested at 7% * Interest rate of 7%) = (y * 7/100) = 0.07y
According to the problem, the total income from both investments is 1,410 pesos, so we have the equation:
0.05x + 0.07y = 1,410 ---- (equation 2)
We now have a system of equations:
x + y = 25,000 ---- (equation 1)
0.05x + 0.07y = 1,410 ---- (equation 2)
We can solve this system of equations using various methods like substitution or elimination. Let's use the elimination method.
Multiplying equation 1 by 0.05, we get:
0.05x + 0.05y = 0.05 * 25,000
0.05x + 0.05y = 1,250 ---- (equation 3)
Now, subtracting equation 3 from equation 2, we eliminate the x variable:
(0.05x + 0.07y) - (0.05x + 0.05y) = 1,410 - 1,250
0.07y - 0.05y = 160
0.02y = 160
Dividing both sides by 0.02, we find:
y = 160 / 0.02
y = 8,000
Therefore, the man invested 8,000 pesos at 7% interest.