SOLUTION: Set up a system of linear equations and solve for the indicated quantities. Nathan buys a combination of 45 cents stamps and 65 cents stamps at the post office. If he spends e

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Question 1108895: Set up a system of linear equations and solve for the indicated quantities.

Nathan buys a combination of 45 cents stamps and 65 cents stamps at the post office. If he spends exactly $24.50 on 50 stamps, how many of each type did he buy?

Found 2 solutions by MathLover1, ikleyn:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

Nathan buys a combination of 45 cents stamps and 65 cents stamps at the post office. If he spends exactly $24.50 on 50 stamps, how many of each type did he buy?
let 45+cents stamps be x and 65 cents stamps y
first convert cents to dollars:
45+cents = $0.45+
65+cents = $0.65+
if Nathan buys 50 stamps , we have
x%2By=50.....eq.1

If he spends exactly $24.50 on all stamps, we have
0.45x%2B0.65y=24.50.....eq.2
solve the system:
x%2By=50.....eq.1
0.45x%2B0.65y=24.50.....eq.2
----------------------------------------
x%2By=50.....eq.1 ...solve for x
x=50-y.....eq.1a...substitute in eq.2
0.45%2850-y%29%2B0.65y=24.50.....eq.2..solve for y
22.5-0.45y%2B0.65y=24.50
0.2y=24.50-22.5
0.2y=2
y=2%2F0.2
y=10
now go back to eq.1a and solve for x
x=50-y.....eq.1a
x=50-10
x=40
Nathan did buy 40 of 45+cents stamps, and 10 of 65+cents stamps


Answer by ikleyn(52887) About Me  (Show Source):
You can put this solution on YOUR website!
.
There is about one thousand solved word problems in this site on establishing and solving systems of 2 equations in 2 unknowns.

See the lessons
    - Oranges and grapefruits
    - Using systems of equations to solve problems on tickets
    - Three methods for solving standard (typical) problems on tickets
    - Using systems of equations to solve problems on shares
    - Using systems of equations to solve problems on investment
    - Two mechanics work on a car
    - The Robinson family and the Sanders family each used their sprinklers last summer
    - Roses and vilolets
    - Counting calories and grams of fat in combined food
    - HOW TO algebreze and solve this problem on 2 equations in 2 unknowns
    - One unusual problem to solve using system of two equations
    - Solving mentally word problems on two equations in two unknowns
    - OVERVIEW of lessons on solving systems of two linear equations in two unknowns

Also,  you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic "Systems of two linear equations in two unknowns".


Save the link to this online textbook together with its description

Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson

to your archive and use it when it is needed.