During summer vacation, Sanjay writes letters and postcards to his friends at home. A letter costs $0.41 to mail and a postcard costs $0.21 to mail. Sanjay writes to 8 friends and spends $2.08. How many letters and postcards he sends.
.41 L + .21 (8-L)= 2.08
.41 L + 1.68 - .21 L = 2.08
.20 L = .40
L = 2
p = 8-L = 6
To solve this problem, let's assume Sanjay sends x letters and y postcards.
The cost of mailing x letters is 0.41x.
The cost of mailing y postcards is 0.21y.
According to the problem, the total cost of mailing is $2.08. So we have the equation:
0.41x + 0.21y = 2.08
We also know that Sanjay sends letters to 8 friends, so x must be less than or equal to 8. Since he is sending letters to his friends, it is possible that he might not be sending any postcards. Therefore, y can be any non-negative value.
Now, we can solve this equation using various methods, such as substitution or elimination. Let's use elimination in this case:
Multiply the first equation by 21 to eliminate the decimals:
21 * (0.41x) + 21 * (0.21y) = 21 * 2.08
8.61x + 4.41y = 43.68
Now we have the following system of equations:
8.61x + 4.41y = 43.68 (Equation 1)
0.41x + 0.21y = 2.08 (Equation 2)
Let's solve it using elimination. Multiply Equation 2 by 21 to eliminate the decimals:
21 * (0.41x) + 21 * (0.21y) = 21 * 2.08
8.61x + 4.41y = 43.68
Now we can subtract Equation 2 from Equation 1:
(8.61x + 4.41y) - (8.61x + 4.41y) = 43.68 - 43.68
0 = 0
This means the two equations are actually the same. They represent the same line, so there are infinitely many solutions. In other words, there are multiple combinations of x and y that satisfy the equation.
Therefore, there are multiple ways Sanjay can send letters and postcards to his 8 friends and spend $2.08.