Jason went to the post office and bought both 41-cent stamps and 26-cent postcards and spent $10.28. The number of stamps was 4 more than twice the number of postcards. How many of each did he buy?
If there were x postcards, then there were 2x+4 stamps.
Now add up the costs -- it totals 10.28
26x + 41(2x+4) = 1026.
Correction: change 1026 to 1028.
To solve this problem, we need to set up a system of equations. Let's define the variables:
Let's say:
x = the number of 41-cent stamps
y = the number of 26-cent postcards
We are given two pieces of information:
1) Jason spent $10.28 at the post office. We can write this information as an equation:
0.41x + 0.26y = 10.28
2) The number of stamps was 4 more than twice the number of postcards. We can also write this information as an equation:
x = 2y + 4
Now, we have a system of equations:
Equation 1: 0.41x + 0.26y = 10.28
Equation 2: x = 2y + 4
To solve this system of equations, we can use substitution or elimination. Let's use substitution:
Substitute the value of x from Equation 2 into Equation 1:
0.41(2y + 4) + 0.26y = 10.28
0.82y + 1.64 + 0.26y = 10.28
1.08y + 1.64 = 10.28
1.08y = 10.28 - 1.64
1.08y = 8.64
y = 8.64 / 1.08
y = 8
Now, substitute the value of y into Equation 2 to find x:
x = 2(8) + 4
x = 16 + 4
x = 20
Therefore, Jason bought 20 of the 41-cent stamps and 8 of the 26-cent postcards.