Solve the problem using a system of equations

Question

A box contains $24.56 in pennies, dimes, and quarters. There are 338 coins in all, with 25 more quarters than dimes. How many pennies are there?

Answer 1

Assign variables for pennies, dimes, and quarters.

 

Let number of pennies = x

Let number of dimes = y

Let number of quarters = y + 25

 

 

Set up equations for total coins.

 

x + y + y + 25 = 338

x + 2y = 313                 eq1

 

Set up equation for total amount.

 

0.01x + 0.10y + 0.25(y + 25) = 24.56

0.01x + 0.10y + 0.25y + 6.25 = 24.56

0.01x + 0.35y = 18.31                             eq2

 

These will be our equations to work with.

 

x + 2y = 313                              eq1

0.01x + 0.35y = 18.31                  eq2

 

 

Multiply eq1 by 0.01.

 

0.01x + 0.02y = 3.13            eq1

0.01x + 0.35y = 18.31            eq2

 

 

Subtract eq2 from eq1 to eliminate the x terms.

 

-0.33y = -15.18

 

y = 46

 

Substitute this value of y into eq1.  This will allow use to solve for x.

 

 

x + 2(46) = 313

x + 92 = 313

x = 221

 

Since the variable x represents the number of pennies, there are 221 pennies.