The price of Darjeeling tea (in rs./kg) is 100 + 0.10 n, on the nth day of 2007 (n = 1, 2, ..., 100), and then remains constant. On the other hand, the price of Ooty tea (in rs./kg) is 89 + 0.15n, on the nth day of 2007 (n = 1, 2, ..., 365). On which date in 2007 will the prices of these two varieties of tea be equal?
Question
The price of Darjeeling tea (in rs./kg) is 100 + 0.10 n, on the nth day of 2007 (n = 1, 2, ..., 100), and then remains constant. On the other hand, the price of Ooty tea (in rs./kg) is 89 + 0.15n, on the nth day of 2007 (n = 1, 2, ..., 365). On which date in 2007 will the prices of these two varieties of tea be equal?
Solution
To find out the date when the prices of Darjeeling and Ooty tea will be equal, we need to set the two equations equal to each other and solve for n.
The price of Darjeeling tea is given by the equation: Pd = 100 + 0.10n The price of Ooty tea is given by the equation: Po = 89 + 0.15n
Setting these two equations equal to each other gives:
100 + 0.10n = 89 + 0.15n
Solving for n, we subtract 0.10n from both sides to get:
0.05n = 11
Then, divide both sides by 0.05 to solve for n:
n = 11 / 0.05 = 220
So, the prices of Darjeeling and Ooty tea will be equal on the 220th day of 2007.
To find the date, we know that the 220th day falls in the month of August. Subtracting the total number of days in the first seven months (31 + 28 + 31 + 30 + 31 + 30 + 31 = 212) from 220, we get 8.
Therefore, the prices of the two teas will be equal on August 8, 2007.
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