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Joe has $4.52 in dimes, nickels, and pennies. If he has one more dime than three times the number of nickels and 10 more pennies than nickels, how many of each type of coin does he have?

Respuesta :

calculista

Answer:

12 nickels, 37 dimes and 22 pennies

Step-by-step explanation:

Let

x ----> the number of nickels

y ----> the number of dimes

z ----> the number of pennies

we know that

1 nickel=$0.05

1 dime=$0.10

1 pennies=$0.01

so

0.05x+0.10y+0.01z=4.52 -----> equation A

y=3x+1 ----> equation B

z=x+10 ----> equation C

substitute equation B and equation C in equation A and solve for x

[tex]0.05x+0.10(3x+1)+0.01(x+10)=4.52 0.05x+0.30x+0.10+0.01x+0.10=4.52\\0.36x+0.20=4.52\\ 0.36x=4.52-0.20\\x=4.32/0.36\\x=12\ nickels[/tex]

Find the value of y

[tex]y=3(12)+1=37\ dimes[/tex]

Find the value of z

[tex]z=12+10=22\ pennies[/tex]

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