use systems of linear equations in two variables to solve problems

Question

Solve this problem using systems of linear equations in two variables:

 

Luis and Julia have the same number of coins. Luis has only dimes and Julia has only quarters. If Julia has $1.80 more than Luis does, how many coins does each have?

Answer 1

Let D = number of dimes that Luis has

Let Q = number of quarters that Julia has

 

They have the same number of coins, so D = Q

 

The value of the dimes is 0.10D, and the value of the quarters is 0.25Q

 

The value of the quarters is $1.80 more than the dimes, so 0.25Q = 0.10D + 1.80

 

Since D = Q we can write this as 0.25Q = 0.10Q + 1.80, so

 

0.15Q = 1.80

 

Q = 1.80 / 0.15 = 180 / 15 = 12 

 

D = Q = 12

 

So they each have 12 coins

 

Check : D =12, Q = 12, so D = Q

Check : 0.25Q = 0.25(12) = 3.00 

   and    0.10D = 0.10(12) = 1.20, so Julia has $1.80 more than Luis