Question

Mr.marichal has quarters ,dimes,and pennies in a jar.he has twice as many quarters as oennies.he also has 5 more dimes than pennies.the total value of the coins is $6.60.how many of each type of coin does he have

Answer 1

He has 20 quarters, 15 dimes and 10 pennies.

Step-by-step explanation:

Let,

Quarters = x

Dimes = y

Pennies = z

We know that,

A quarter is 25 cents, dime is 10 cents and penny is 1 cent.

Total amount = $6.60 = 6.60*100 = 660 cents

According to given statement;

25x+10y+z=660   Eqn 1

x=2z    Eqn 2

y=z+5   Eqn 3

Putting these values of x and y in Eqn 1

$25(2z)+10(z+5)+z=660\\50z+10z+50+z=660\\61z=660-50\\61z=610$

Dividing both sides by 61;

$\frac{61z}{61}=\frac{610}{61}\\z=10$

Putting z=10 in Eqn 2

$x=2(10)\\x=20$

Putting z=10 in Eqn 3

$y=10+5\\y=15$

He has 20 quarters, 15 dimes and 10 pennies.

Keywords: linear equations, substitution method

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