Question

Pedro le dice a María si cambias los billetes de 10 € que tienes por billetes de 5 € y los billetes de 5 € por billetes de 10 € seguirás teniendo el mismo dinero cuánto dinero tiene María si en total son 20 billetes

Answer 1

Answer: Maria has 10 bills of 5€ and 10 bills of 10€.

She has a total of 150€.

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:

`\left \{ {{f+t=20} \atop {5f+10t=10f+5t}} \right.`

Use the Substitution method to solve the system of equations:

1. Solve for "f" from the first equation:

`f=20-t`

2. Substitute the equation obtained into the second equation and solve for "t".

Then:

`5(20-t)+10t=10(20-t)+5t\\\\100-5t+10t=200-10t+5t\\\\20t-10t=100\\\\t=(100)/(10)\\\\t=10`

3. Substitute the value of "t" into the equation
`f=20-t` and evaluate:

`f=20-10\\\\f=10`

Therefore, Maria has 10 bills of 5€ and 10 bills of 10 €.

So the total amount of money she has, is:

`Total=10(5)+10(10)=150`

She has a total of 150€.