Question

Marcos ahorro $3270 en monedas de $10,$5 y $2.Si el numero de monedas de $10 excede en 20 a las de $5 y en 15 a las de $2.

Cuantas monedas de 5 tiene Marcos?

Marcos saved $ 3270 in $ 10, $ 5 and $ 2 coins. If the number of $ 10 coins exceeds $ 5 in $ 5 and $ 2 in 15.
How many 5 coins does Marcos have?

Answer 1

The number of $5 coins is 180

Explanation:

Let

x ---> the number of $10 coins

y ---> the number of $5 coins

z ---> the number of $2 coins

we know that

`10x+5y+2z=3,270` -----> equation A

`x=y+20` ---->
`y=x-20` ----> equation B

`x=z+15` ---->
`z=x-15` ----> equation C

Solve the system by substitution

Substitute equation B and equation C in equation A

`10x+5(x-20)+2(x-15)=3,270`

solve for x

`10x+5x-100+2x-30=3,270`

`17x-130=3,270`

`17x=3,270+130`

`17x=3,400`

`x=200`

Find the value of y

`y=x-20`

`y=200-20=180`

therefore

The number of $5 coins is 180