Question 160966
Amanda has some pennies, nickels, dimes, and quarters in her piggy bank. There is more than $1.50 and less than $2.25. Using the clues, determine how much money Amanda has.
:
Write an equation for each statement:
:
"-there are 4 times as many nickels as quarters"
n = 4q
:
"-there are twice as many quarters as dimes"
q = 2d
:
"-there is an equal number of pennies and dimes"
p = d
:
Write a total$ 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 = {{{2/1.01}}} 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 = {{{2.02/1.01}}}
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?