Joan has an equal number of dimes and quarters with a total value of $1.40 . how many coins does she have altogether? (a dime = .10, and a quarter = .25

First, let's define the variables d and q as follows:

d: total number of dimes
q: total number of quarters.

"Joan has an equal number of dimes and quarters" means that d=q.

"...with with a total value of $1.40" means that

                                0.1 d + 0.25 q =1.40.  ***

This is because Joan has a total of d dimes each with a value of 0.1$, and a total of q quarters, each with a value of 0.25.

Since d=q, we can write the equation *** as:

0.1 q +0.25 q=1.40

        0.35 q=1.40

              q=1.40/0.35 = 4.

Thus, Joan has a total of 4 quarters, and 4 dimes.

8 coins.