There are 16 coins in a bank. if the coins are all nickels and dimes and they total $1.05, how many nickels are there

STEP 1
determine quantity and cost equations

x= number of nickels
y= number of dimes

QUANTITY EQUATION
x + y= 16

COST EQUATION
each nickel= $0.05
each dime= $0.10

$0.05x + $0.10y= $1.05

STEP 2
multiply quantity equation by -0.10

-0.10(x + y)= -0.10(16)
-0.10x - 0.10y= -1.60

STEP 3
using the elimination method, add the cost equation and step 1 equation to eliminate the y term and solve for x

0.05x + 0.10y= 1.05
-0.10x - 0.10y= -1.60
y term cancels out

-0.05x= -0.55
divide both sides by -0.05

x= 11 nickels

STEP 4
substitute x value in either original equation

x + y= 16
11 + y= 16
y= 5 dimes

CHECK
$0.05x + $0.10y= $1.05
0.05(11) + 0.10(5)= 1.05
0.55 + 0.50= 1.05
1.05= 1.05

ANSWER: There are 11 nickels and 5 dimes.

Hope this helps! :)

Step-by-step explanation: