Julie went to the post office and bought both $0.41
stamps and $0.26 postcards. She spent $51.40. The
number of stamps was 20 more than twice the number
of postcards. How many of each did she buy?
I just want to know how to set it up.
It's 100 multiplied by $ 0.41 + 40 multiplied by $ 0.26
If done right, You should have 41 + 10.4 = 51.40.
41*(stamps)+.26*(post)=51.4
1 stamp=20+2(post)
0.41*20+2(post)+.26=51.4
Post=40
stamps= 20+2x40
Well, let's break it down, clown style! 🎪
Let's say Julie bought x postcards and y stamps. Here's what we know:
1) The cost of one stamp is $0.41.
2) The cost of one postcard is $0.26.
3) The total amount spent was $51.40.
So, we can set up two equations:
Equation #1: x postcards + y stamps = Total spent
0.26x + 0.41y = 51.40
Equation #2: y stamps = 2x + 20
(Notice it says the number of stamps is 20 more than TWICE the number of postcards)
Now, let's solve this merrily! 🎉
10
To set up and solve this problem, we can use a system of equations approach. Let's assign variables to represent the unknown quantities:
Let's say the number of stamps Julie bought is represented by 's', and the number of postcards she bought is represented by 'p'.
We know that the price of each stamp is $0.41 and the price of each postcard is $0.26.
From the given information, we can create two equations:
Equation 1: The total amount spent on stamps and postcards is $51.40:
0.41s + 0.26p = 51.40
Equation 2: The number of stamps is 20 more than twice the number of postcards:
s = 2p + 20
Now we have a system of equations, and we can solve for the variables 's' and 'p'. We can use the substitution or elimination method to solve this system of equations.
Using substitution, we can substitute the value of 's' from Equation 2 into Equation 1:
0.41(2p + 20) + 0.26p = 51.40
Now we can simplify and solve for 'p' by distributing and combining like terms:
0.82p + 8.2 + 0.26p = 51.40
1.08p + 8.2 = 51.40
1.08p = 51.40 - 8.2
1.08p = 43.20
p = 43.20 / 1.08
p ≈ 40
Now that we have the value of 'p', we can substitute it back into Equation 2 to find the value of 's':
s = 2p + 20
s = 2(40) + 20
s = 80 + 20
s = 100
Therefore, Julie bought 40 postcards and 100 stamps.