John M. answered • 10/29/13

John - Algebra Tutor

AMIE Q.

asked • 10/29/13bobbie has 1.54 in quarters, dimes, nickels, and pennies. he has twice as many dimes as quarters and three times as many nickels as dimes. The number of pennies is the same as the number of dimes. How many of each coin does he have?

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John M. answered • 10/29/13

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John - Algebra Tutor

Define Variable

d = dimes

q = quarters

n = nickels

p = pennies

Given relationships

2 dimes for each quarter

3 nickels for each dime

Same number of pennies and dimes

Problem

Find the number and types of coins that total $1.54

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including the values of the coins and putting it in terms of addition

.25q+.1d+.05n+.01p=1.54

because of the total, there must be at least 4 pennies. Starting there and applying the relationships, if we have 4 pennies, then there are 4 dimes and 2 quarters and 12 nickels. If we total these coins,

2 quarter = 0.50

4 dimes = 0.40

12 nickels = 0.60

4 pennies = 0.04

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1.54 (the desired value)

My approach here is to logically apply the given relationships and coin values to find the solution.

To solve this system let

q = number of quarters

d = number of dimes

n = number of nickels

p = number of pennies.

Since the total amount of money (in pennies) is 154 we have

25 q + 10 d + 5 n + p = 154

We also have d = 2 q ; n = 3 d ; d = p

These last three equations can be rearranged to :

q = p/2 ; n = 3 p ; d = p These can then be substituted into the first equation to get

25 (p/2) + 10 p + 15 p + p = 154 A factor of p can be taken out of the left side to get

[25/2 +10 + 15 + 1] p = (77/2) p = 154 and so

p = 4

From there we can work back to get d = 4 ; n = 12 ; q =2. This does check out.

Vivian L. answered • 10/29/13

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Microsoft Word/Excel/Outlook, essay composition, math; I LOVE TO TEACH

Hi again Amie;

$1.54=154 cents.

It would be easier to work in cents than dollars.

D=2Q

3D=N

D=D

D=P

We know the student has at least 4 pennies.

D=2Q=2(25)=50 cents

3D=N=12(5)=60 cents

D=D=4(10)=40 cents

D=P=4(1)=4 cents

3D=N=12(5)=60 cents

D=D=4(10)=40 cents

D=P=4(1)=4 cents

TOTAL...154 cents

Hi Amie, Let x=number of quarters. then 2x=number of dimes and pennies. and 6x=number of nickels.

Now using the value of each we have the equation...

x(.25)+2x(.10)+6x(.05)+2x(.01)=1.54

.25x+.2x+.3x+.02x=1.54

.77x=1.54

x=2 So we have 2 quarters, 4 dimes, 12 nickels and 4 pennies.

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