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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

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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.
 
 
 

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