Question 717739
Let c = number of coins each has.
Let L = the value of Luis' coins, in cents
Let J = value of Julia's coins, in cents
Then we have
(1) J - L = 180
where we use 180 cents instead of $1.80.
Since Luis has only dimes, the value of his coins is 10*c, and Julia's quarters are worth 25*c. Put L and J into (1) to get
(2) 25*c - 10*c = 180 or
(3) 15*c = 180 or
(4) c = 12
Let's check this value using (1).
Is (25*12 - 10*12 = 180)?
Is (300 - 120 = 180)?
Is (180 = 180)? Yes
Answer: Luis and Julia each have 12 coins.