Question 58285
Hello Ashley,

we can solve this question by setting up a set of linear equations.

let the nickels be x and dimes be y

since we have 50 coins both x+y=50
because their face value is .05 and .1 and they add up to 3.50 we can state .05x+.1y=3.50

now we can solve
x+y=50
.05x+.1y=3.50
isolate y in the bottom equation

.05x+.1y=3.50
subtract .05x
.1Y=3.5-.05x
divide by .1
y=35-.5X
now you can substitute in the equation for y in the first equation.

x+(35-.5x)=50
you can simplify the equation
.5x+35=50
subtract 35 from each side
.5X=15
now divide by .5
x=30

there are 30 nickels, since you have 50 coins, you have 20 dimes as well.

we can check this answer

30(.05)+20(.10)=
$1.5+2.0=$3.50