Valentina has $2.90 of change in her pocket. She has only 20 cent and 59 cent coins, 7 coins in total. If t is the number of 20c coins that Valentina has, find t.

First, I must assume that you mean 50-cent coins, since the 59-cent coin does not exist and besides doing so, it does not give an exact number of coins.

To calculate the value of t, you must first consider some equations where it is included.

First, the total value of Valentina's money. It should also include the number of 50 cent coins, I will call it "s". The equation would be the following (considering that 1 $ is 100c):

20 * t + 50 * s = 290 (1)

We can add another equation that mentions the statement that says there are 7 currencies, therefore:

t + s = 7 (2)

If I clear this equation, as follows:

s = 7-t (3)

I can replace it in my first equation, and it would be as follows:

20 * t + 50 * (7-t) = 290 (4)

The development of the equation is as follows:

20 * t + 50 * 7 -5 * t = 290

20 * t + 350 - 50 * t = 290, rearranging the equation

20 * t - 50 * t = 290 - 350

-30 * t = -60

t = -60 / -30

t = 2

So the value of t is 2 cents.

Now the number of 50 cents coins would be

s = 7 - t, replacing the value of t

s = 7 - 2 = 5

Then it would be 2 coins of 20 cents and 5 coins of 50 cents.

Checking the answer:

2 * 20 + 50 * 5 = 40 +250 = 290