Final answer:
Ari has a total of 22 coins made up of pennies and nickels. By setting up two equations based on the number of coins and their total value and solving them simultaneously, we find that Ari has 14 pennies.
Step-by-step explanation:
The student is asked to determine how many pennies Ari has if he has a total of 22 coins consisting of pennies (p) and nickels (n). The total value of the coins is $0.54. To organize the information, we use two equations based on the given data:
- The total number of coins is 22, so p + n = 22.
- The total value of the coins is $0.54. Since pennies are worth $0.01 each and nickels are worth $0.05 each, we can write this as 0.01p + 0.05n = 0.54.
We can now solve these two equations simultaneously. We already have p + n = 22, which we can rearrange to n = 22 - p. Substituting n from this equation into the second equation gives us:
0.01p + 0.05(22 - p) = 0.54.
Multiplying out the brackets we get:
0.01p + 1.10 - 0.05p = 0.54,
which simplifies to:
1.10 - 0.04p = 0.54.
Subtracting 1.10 from both sides gives us:
-0.04p = -0.56,
and dividing by -0.04 we find:
p = 14.
So, Ari has 14 pennies.