SOLUTION: Heather has $2.50 in nickels, dimes and quarters. She has three times as many nickels as dimes and four times as many quarters as dimes. a. Write an equation that relates the numb

Question 588029: Heather has $2.50 in nickels, dimes and quarters. She has three times as many nickels as dimes and four times as many quarters as dimes.
a. Write an equation that relates the number of each kind of coin to the amount of money that Heather has.
b. How many of each kind of coin does heather have?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Heather has $2.50 in nickels, dimes and quarters.
She has three times as many nickels as dimes and four times as many quarters as dimes.
a. Write an equation that relates the number of each kind of coin to the amount of money that Heather has.
:
The total value equation
.05n + .10d + .25q = 2.50
"three times as many nickels as dimes"
n = 3d
"four times as many quarters as dimes."
q = 4d
;
:
b. How many of each kind of coin does heather have?
:
.05n + .10d + .25q = 2.50
replace n and q using the above equations
.05(3d) + .10d + .25(4d) = 2.50
.15d + .10d + 1.00d = 2.50
1.25d = 2.50
d = 2.50/1.25
d = 2 dimes
then
n = 3(2)
n = 6 nickels
and
q = 4(2)
q = 8 quarters
:
:
Check these solution in the value equation
.05(6) - .10(2) + .25(8) =
.30 = .20 + 2.00 = 2.50
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