Write an equation for each situation then use the equation to solve the problem

Question

Sierra has a total of 61 dimes and quarters in her piggybank. She has 3 more quarters than dimes. The coins have a total value of $10.90. How many dimes and how many quarters does she have? 

Answer 1

Hello Quinn,

 

First, denote the number of dimes as x, and the number of quarters as y.

 

Since the total number of coins equals 61, we can write the following equation:  x + y = 61

 

Since the total value of the coins equals $10.90, and we know that a quarter is worth $0.25 and a dime is worth $0.10, the total value can be expressed as a function of the number of quarters and dimes:  $0.10*x + $0.25*y = $10.90

 

Now, we have two equations and two variables, meaning we can solve the 2x2 system! 

 

Rewrite the first equation in terms of x: x = 61 - y

 

Now substitute this expression into the second equation: $0.10*(61-y) + $0.25*y = $10.90

 

Solve for y: $.15*y = $4.80,  y = 32

 

Substitute back into the first equation to get x: x = 29

 

She indeed has 3 more quarters than dimes since 32-29= 3, so we did it right (: 

 

If you found this helpful and would like a more in-depth breakdown of how I set up the equations, please contact me so we can set up a tutoring lesson!