SOLUTION: Amanda has some pennies, nickels, dimes, and quarters in her piggy bank. There is more than $1.50 and less than $2.25. Using the clues, determine how much money Amanda has. -the

Question 160966: Amanda has some pennies, nickels, dimes, and quarters in her piggy bank. There is more than $1.50 and less than $2.25. Using the clues, determine how much money Amanda has.
-there are 4 times as many nickels as quarters
-there are twice as many quarters as dimes
-there is an equal number of pennies and dimes
Thank you for you help!!
Found 2 solutions by ptaylor, ankor@dixie-net.com:
Answer by ptaylor(2198) (Show Source): You can put this solution on YOUR website!
OK, we'll let x=number of dimes
Then x=number of pennies, also
And 2x=number of quarters
And 4*2x=8x=number of nickels
Now we can set up our equation (or inequality) to solve:
(Lets deal in pennies to get rid of the decimals)
150<(x+10x+5*8x+25*2x)<225 simplifying
150<(x+10x+40x+50x)<225 collecting like terms, we have:
150<(101x)<225 divide each term by 101
1.48<(x)<2.23 since we cannot have a fraction of a coin, x has no choice but to be 2
For x=2, we have
2 pennies 2*1=2
2 dimes 2*10=20
4 quarters 4*25=100
16 nickels 16*5=80
TOTAL-------202 or $2.02 cents
And this satisfies the inequality
Hope this helps---ptaylor
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Amanda has some pennies, nickels, dimes, and quarters in her piggy bank. There is more than $1.50 and less than $2.25. Using the clues, determine how much money Amanda has.
:
Write an equation for each statement:
:
"-there are 4 times as many nickels as quarters"
n = 4q
:
"-there are twice as many quarters as dimes"
q = 2d
:
"-there is an equal number of pennies and dimes"
p = d
:
Write a total$ equation within the given range
.01p + .05n + .10d + .25q = 2.00
:
try to get everything in terms of d:
In the 1st equation, substitute 2d or q (from the 2nd equation)
n = 4(2d)
n = 8d
:
Substitute:
.01d + .05(8d) + .10d + .25(2d) = 2.00
.01d + .40d + .10d + .50d = 2
1.01d = 2
d = obviously not a solution (has to be an integer)
:
Make a solution by multiplying 1.01 * 2, so the total is $2.02, then we have:
d =
d = 2 dimes
then
.01(2) + .40(2) + .10(2) + .50(2) = 2
.02 + .80 + .20 + 1.00 = $2.02
:
Find the number of each coin using d = 2:
p = d; 2 pennies
n = 8d: 16 nickels
d = 2 dimes
q = 2d; 4 quarters
;
:
Confirm solution from this:
.01(2) + .05(16) + .10(2) + .25(4) =
.02 + .80 + .20 + 1.00 = $2.02 is Amanda's total
:
There are probably other ways to do this. Did this make sense to you?

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