A beach apartment rented for Rs. 5000 per month during the 3 summer months and for Rs. 1800 per month during the remainder of the year. During 1 year, it was occupied for only 9 months, and rentals amounted to Rs. 22600.
To find the number of months the apartment was rented during the summer and the number of months rented during the remainder of the year, we can use algebraic equations.
Let's assume that the number of months the apartment was rented during the summer is x, and the number of months rented during the remainder of the year is y.
According to the given information, the rent during the summer months is Rs. 5000 per month, and the rent during the remainder of the year is Rs. 1800 per month.
We can write the following equations based on the given information:
1. x + y = 9 (as the apartment was occupied for only 9 months in total)
2. 5000x + 1800y = 22600 (as the total rental amount for the year is Rs. 22600)
Now, we have a system of two equations that we can solve simultaneously to find the values of x and y.
To solve this system of equations, we can use the method of substitution or elimination. Let's use the method of substitution in this case:
From equation 1, we can write x = 9 - y.
Substituting this value of x into equation 2, we get: 5000(9 - y) + 1800y = 22600.
Expanding and simplifying the equation, we have: 45000 - 5000y + 1800y = 22600.
Combining like terms, we get: -3200y = -22400.
Dividing both sides of the equation by -3200, we get: y = 7.
Now, substitute this value of y back into equation 1 to find the value of x:
x + 7 = 9.
Subtracting 7 from both sides of the equation, we get: x = 2.
Therefore, the apartment was rented for 2 months during the summer (x) and 7 months during the remainder of the year (y).
sounds like a good deal.
was there a question somewhere in there?