Amy bought 18 stamps. Some were for postcards and cost 35 cents. The others were for regular mail and cost 49 cents. She spent $7.28 on the stamps. How many of each did she buy?
p + r = 18
35p + 49r = 728
solve the system by substitution or elimination
To find out how many stamps Amy bought for postcards and regular mail, we can use a system of equations. Let's assume that she bought "x" stamps for postcards and "y" stamps for regular mail.
From the given information, we know that the cost of postcard stamps is $0.35 and regular mail stamps are $0.49. We also know that Amy bought a total of 18 stamps and spent a total of $7.28.
Using this information, we can set up the following system of equations:
Equation 1: x + y = 18 (total number of stamps bought)
Equation 2: 0.35x + 0.49y = 7.28 (total cost of stamps)
Now, let's solve this system of equations to find the values of x and y.
First, let's multiply Equation 1 by 0.35 (the cost of postcard stamps) to eliminate x from Equation 2:
0.35x + 0.35y = 6.3
Now, subtract this equation from Equation 2 to eliminate x:
(0.35x + 0.49y) - (0.35x + 0.35y) = 7.28 - 6.3
0.49y - 0.35y = 0.98
0.14y = 0.98
Dividing both sides by 0.14, we get:
y = 7
Now, substitute the value of y back into Equation 1 to find x:
x + 7 = 18
Subtracting 7 from both sides, we get:
x = 11
Therefore, Amy bought 11 stamps for postcards and 7 stamps for regular mail.