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.
:
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