This is a problem of system of linear equations in two variables. This concept of mathematics is very useful in real-life problems. You can solve a system by finding the solution. A solution of a system are the values of the variables that satisfies each equation in the system. So by knowing these concepts we can get a system of equation by analyzing each statement step by step, that is:
1. Alice has a total of 12 dimes and nickels.
Let the variables:
[tex]D: Dimes \\ N:Nickles[/tex]
1st. Equation:
[tex]D+N=12[/tex]
2. She has 2 more nickels than dimes
2nd Equation:
[tex]N=D+2[/tex]
Therefore our system of linear equations is:
[tex](1) \ D+N=12 \\ (2) \ N=D+2 \\ \\ Substituting \ (2) \ in \ (1): \\ D+(D+2)=12 \therefore 2D=10 \therefore D=5 \\ \\ Solving \ for \ N \ in \ (2): \\ N=5+2=7[/tex]
Conclusion:
Alice has 5 dimes and 7 nickels.
