A painter charges 10 naira for painting a single digit on a wall. Houses in a village are numbered starting from 1. If a total of 1950 naira was given to the painter, how many houses are there in the village?
Let's assume there are x houses in the village.
If the painter charges 10 naira for painting a single digit, then painting a house with a single-digit number would cost 10 naira.
To find the total number of houses, we need to find the sum of all the costs.
The sum of the costs for all the houses in the village can be calculated using the formula for the sum of an arithmetic series:
Sum = (n/2)(first term + last term)
The first term is the cost of painting the house with the number 1, which is 10 naira.
The last term is the cost of painting the house with the number x, which is 10x naira.
So the sum of the costs for all the houses is:
1950 = (x/2)(10 + 10x)
To simplify the equation, we can divide both sides by 10:
195 = (x/2)(1 + x)
Next, we can multiply both sides by 2 to get rid of the fraction:
390 = x(1 + x)
Now we have a quadratic equation. Let's rearrange it:
0 = x^2 + x - 390
Factoring this equation gives:
0 = (x + 26)(x - 15)
So either x + 26 = 0 or x - 15 = 0.
Solving these equations gives:
x = -26 or x = 15
Since the number of houses cannot be negative, we discard x = -26 and conclude that there are 15 houses in the village.