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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?

Respuesta :

calculista

Answer:

The number of $5 coins is 180

Step-by-step explanation:

Let

x ---> the number of $10 coins

y ---> the number of $5 coins

z ---> the number of $2 coins

we know that

[tex]10x+5y+2z=3,270[/tex] -----> equation A

[tex]x=y+20[/tex] ----> [tex]y=x-20[/tex] ----> equation B

[tex]x=z+15[/tex] ----> [tex]z=x-15[/tex] ----> equation C

Solve the system by substitution

Substitute equation B and equation C in equation A

[tex]10x+5(x-20)+2(x-15)=3,270[/tex]

solve for x

[tex]10x+5x-100+2x-30=3,270[/tex]

[tex]17x-130=3,270[/tex]

[tex]17x=3,270+130[/tex]

[tex]17x=3,400[/tex]

[tex]x=200[/tex]

Find the value of y

[tex]y=x-20[/tex]

[tex]y=200-20=180[/tex]

therefore

The number of $5 coins is 180

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