Answer: Maria has 10 bills of 5€ and 10 bills of 10€.
She has a total of 150€.
Step-by-step explanation:
Let be "f" the number of 5€ bills that Maria has and "t" the number of 10€ bills that Maria has.
Set up a system of equations:
[tex]\left \{ {{f+t=20} \atop {5f+10t=10f+5t}} \right.[/tex]
Use the Substitution method to solve the system of equations:
1. Solve for "f" from the first equation:
[tex]f=20-t[/tex]
2. Substitute the equation obtained into the second equation and solve for "t".
Then:
[tex]5(20-t)+10t=10(20-t)+5t\\\\100-5t+10t=200-10t+5t\\\\20t-10t=100\\\\t=\frac{100}{10}\\\\t=10[/tex]
3. Substitute the value of "t" into the equation [tex]f=20-t[/tex] and evaluate:
[tex]f=20-10\\\\f=10[/tex]
Therefore, Maria has 10 bills of 5€ and 10 bills of 10 €.
So the total amount of money she has, is:
[tex]Total=10(5)+10(10)=150[/tex]
She has a total of 150€.
