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.