melinda has nickles and quarters in her bank. She has 8 fewer nickles than quarters. Her total is $3.20 how many of each coin does she have

*Melinda has nickles and quarters in her bank. She has 8 fewer nickles than quarters. Her total is $3.20 how many of each coin does she have?*

Step 1 - Identify and label the unkhowns

*How many of each coin (nickles and quarters) does she have?*

Let x = the number of nickles that Melinda has in her bank

Let y = the number of quarters she has in her bank

Step 2 - There are two unknowns (x and y), so we need two equations to solve for the unknowns.

Equation 1

*She has 8 fewer nickles than quarters*Number of nickles (x) = Number of quarters (y) minus 8

x = y - 8

Equation 2

*Her total is $3.20*Each nickles is worth 5 cents or $0.05. Each quarter is worth 25 cents or $0.25

Number of nickles*$0.05 + number of quarters*$0.25 = $3.20

0.05x + 0.25y = $3.20

Step 3 - Substitute y-8 from equation 1 for x in equation 2.

0.05x + 0.25y = $3.20 (Equation 2)

0.05(y-8) + 0.25y = $3.20 (Substitute y-8 for x)

0.05y - (0.05)(8) + 0.25y = $3.20 (Multiply 0.05 across the terms in the ( ))

0.30y = $3.60 ( Add terms)

Solve for y. Then solve for x, where x = y-8.

Step 4 - Check by:

Adding your x and y values into equation 2 (0.05x + 0.25y = $3.20) and verifying they add up to $3.20.