(linear system word problem)
a total of 27 coins, in nickels and dimes, are in a wallet. if the coins total $2.15, how many of each type of coin are there?

11 nickels and 16 dimes

Step-by-step explanation:

Let n and d represent the numbers of nickels and dimes respectively.

As there are 27 coins, n + d = 27, which can be solved for d:  d = 27 - n.

The total values of the coins are represented by:

$0.05n + $0.10d = $2.15.  

Substituting 27 - n for d, we get:

0.05n + 0.10(27 - n) = 2.15 (which is entirely in the variable n).

Performing the indicated multiplication, we get:

0.05n + 2.7 - .10n = 2.15

Next, we consolidate the n terms on the right side and the constants on the left:

0.55 = 0.05n, or

n = 0.55/0.05 = 11

Thus, there are 11 nickels and 27 - 11, or 16, dimes.

20

step-by-step explanation: