Solve the problem.A collection of dimes is arranged in a triangular array with 14 coins in the base row, 13 in the next, 12 in the next, and so forth. Find the value of the collection.

To solve this problem, we need to find the total value of the collection of dimes.

Step 1: Determine the number of dimes in each row.
The number of dimes in each row decreases by 1 as we move up. We can use the formula for the sum of an arithmetic series to find the number of dimes in each row:
First Term (a) = 14 (the number of dimes in the base row)
Common Difference (d) = -1 (since each row has 1 fewer dime than the previous row)
Number of Terms (n) = 14 (the number of rows)

Using the formula for the sum of an arithmetic series:
Sn = (n/2)(2a + (n-1)d)
S14 = (14/2)(2(14) + (14-1)(-1))
S14 = 7(28 + 13(-1))
S14 = 7(28 - 13)
S14 = 7(15)
S14 = 105

So, there are a total of 105 dimes in the collection.

Step 2: Calculate the value of the collection.
Since each dime has a value of $0.10, the total value of the collection can be found by multiplying the number of dimes by the value of each dime:
Value = Number of dimes * Value per dime
Value = 105 * 0.10
Value = $10.50

Therefore, the value of the collection of dimes is $10.50.