Question

jennifers piggy bank contains nickles, dimes, and quarters. she has 4 more dimes then quarters and 3 times as many nickles as dimes. the total value of the couns is $5.00. how many of each kind of coin does she have?

Answer 1

Jennifer have 8 quarters, 12 dimes and 36 nickels.

Step-by-step explanation:

Given,

Worth of coins = $5.00 = 5*100 = 500 cents

One quarter = 25 cents

One dime = 10 cents

One nickel = 5 cents

Let,

x = number of quarters

y = number of dimes

z = number of nickels

According to given statement;

25x+10y+5z=500     Eqn 1

y = x+4                      Eqn 2

z = 3y

z = 3(x+4)    => z = 3x+12   Eqn 3

Putting value of y and z from Eqn 2 and 3 in Eqn 1

$25x+10(x+4)+5(3x+12)=500\\25x+10x+40+15x+60=500\\50x+100=500\\50x=500-100\\50x=400$

Dividing both sides by 50

$\frac{50x}{50}=\frac{400}{50}\\x=8$

Putting x = 8 in Eqn 2

$y=8+4\\y=12$

Putting x=8 in Eqn 3

$z=3(8)+12\\z=24+12\\z=36$

Jennifer have 8 quarters, 12 dimes and 36 nickels.

Keywords: linear equation, substitution method

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