The value of 25 coins, consisting of dimes and quarters, is $ 3.55. How many dimes are in the collection?

18 dimes = 1.80

7 qtrs = 1.75
Total = the $3.55

Can you work it backwards, as I have no idea how to set an equation. It was instinct for me to see that initially I had to break the 55-cents down and then work with the $3.00.

I'm sorry I can't help with setting the equation. JJ

Total number of coins = 25

Number of dimes = x
Number of quarters = 25 - x
Value of 1 dime = .10
Value of 1 quarter = .25
Total value of coins = $3.55

The equation:

.10(x) + .25(25 - x) = 3.55
.10x + 6.25 - .25x = 3.55
-.15x + 6.25 = 3.55
-.15x = -2.7
x = 18 dimes
25 - x = 25 - 18 = 7 quarters

Ok thanks

34.67

To solve this problem, we need to set up an equation based on the information given. Let's call the number of dimes "D" and the number of quarters "Q".

Since the problem states that there are a total of 25 coins, we can write our first equation:

D + Q = 25

Next, we need to use the information that the total value of the coins is $3.55. Since dimes are worth 10 cents each and quarters are worth 25 cents each, we can write our second equation:

10D + 25Q = 355 (all values are in cents)

Now we have a system of two equations:

D + Q = 25
10D + 25Q = 355

We can solve this system of equations using various methods like substitution or elimination.

Let's use the elimination method to solve for D. Multiply the first equation by 10, then subtract it from the second equation:

10D + 10Q = 250
10D + 25Q = 355
----------------------
0D - 15Q = -105

Simplifying the equation, we have:

-15Q = -105

Dividing both sides by -15, we get:

Q = 7

Now that we know the number of quarters is 7, we can substitute this value back into the first equation to find the number of dimes:

D + 7 = 25

Subtracting 7 from both sides, we have:

D = 18

Therefore, there are 18 dimes in the collection.