(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?
Accepted Solution
A:
Answer:11 nickels and 16 dimesStep-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 = 2.15Next, we consolidate the n terms on the right side and the constants on the left:0.55 = 0.05n, orn = 0.55/0.05 = 11Thus, there are 11 nickels and 27 - 11, or 16, dimes.