.
You can start from the system of two equations in two unknowns
x + y = 24 (1) (counting coins)
5x + 25y = 240 (2) (counting cents)
Then you can multiply the first equation by 5 (both sides) to get the system in the equivalent form
5x + 5y = 120 (1')
5x + 25y = 240 (2')
Now you can subtract equation (1') from equation (2'). In this way, you exclude the unknown x, and you get
a single equation for the unknown y:
25y - 5y = 240 - 120
20y = 120
y = = 6.
Answer. 6 quarters and (24-6) = 18 nickels.
Check. 6*25 + 18*5 = 240 cents. ! Correct !
Solved. // The method I used to solve the system is called the "Elimination method".
So, on the way, you learned how to solve the system of equations using the Elimination method.
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For coin problems and their detailed solutions see the lessons in this site:
- 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
- Santa Claus helps solving coin problem
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 attentively and become an expert in this field.
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.