.
The total is 50 + 20 = 70 dollars.
So, if x and y are the numbers of 2-dollar coins and 5-dollar coins respectively,
we can write these two equations
x + y = 23 (1) (counting coins)
2x + 5y = 70 (2) (the total)
Now, there are different methods to solve this system.
The beginners usually use the substitution method, since it is simpler to understand.
So, using this method, express from equation (1) x = 23-y and substitute it into equation (2), replacing x there.
You will get a single equation for y
2*(23-y) + 5y = 70.
Simplify it step by step and solve for y.
46 - 2y + 5y = 70
3y = 70 - 46
3y = 24 ====> y = 24/3 = 8.
Answer. 8 5-dollar coins and the rest, 23-8 = 15 of the 2-dollar coins.
CHECK. 8*5 + 15*2 = 40 + 30 = 70 dollars total. ! Precisely correct !
Solved.
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On coin problems, see the lessons
- Coin problems
- More Coin problems
- Solving coin problems without using equations
- Kevin and Randy Muise have a jar containing coins
- Typical coin problems from the archive
- Three methods for solving standard (typical) coin word problems
- More complicated coin problems
- Solving coin problems mentally by grouping without using equations
- Non-typical coin problems
- Santa Claus helps solving coin problem
- OVERVIEW of lessons on coin word problems
in this site.
You will find there the lessons for all levels - from introductory to advanced,
and for all methods used - from one equation to two equations and even without equations.
Read them and become an expert in solution of coin problems.
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 "Coin problems".
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.