how many nickeks and quaters P

Question

A parking meter contains quaters and nickels worth 10.90. There are 58 coinsin all. Find out how many of each there are

Answer 1

How many nickels and quarters?
A parking meter contains quarters and nickels worth 10.90. There are 58 coins in all. Find out how many of each there are.

 

Step 1 - Identify the Unknowns

Let x = the number of nickels

Let y = the number of quarters

 

Step 2 - we have 2 unknowns (x and y) so we need 2 equations to find the unknowns.

 

Equation 1: There are 58 coins in all

 

x + y = 58

 

Equation 2: A parking meter contains quarters and nickels worth 10.90.  Each quarter is worth $0.25.  Each nickel is worth $0.05

 

($0.05)x + ($0.25)y = $10.90

 

Step 3 - Substitute and solve

 

Solve for x in equation 1

 

x + y = 58           (Equation 1)

x = 58 - y            (Subtract y from both sides)

 

Substitute 58-y for x in equation 2

 

($0.05)x + ($0.25)y = $10.90                     (Equation 2)

($0.05)(58-y) + ($0.25)y = $10.90             (Substitute (58-y) in place of x)

$2.90 - ($0.05)y + ($0.25)y = $10.90      (Multiply terms in parentheses by the ($0.05))

 

($0.20)y = $8.00                      (Subtract $2.90 from both sides, combine the y terms)

 

Solve for y (the number of quarter).  Once you have y, solve for x using x = 58 - y.

 

Step 4 - Check

Make sure x + y add up to 58

Make sure ($0.05)x + ($0.25)y adds up to $10.90