Final answer:
By setting up a system of equations based on the value of nickels and quarters and the fact that there are 12 more nickels than quarters, we find that Liliana has 5 quarters and 17 nickels in her backpack.
Step-by-step explanation:
To solve Liliana’s problem involving nickels and quarters, we need to create a system of equations. One nickel is worth 5 cents, and one quarter is worth 25 cents. Let’s define n as the number of nickels and q as the number of quarters.
Since Liliana has $2.10 in total, and there are 100 pennies in one dollar, that means she has 210 pennies worth of coins. This can be expressed mathematically as:
5n + 25q = 210
It is also given that Liliana has 12 more nickels than quarters, which gives us another equation:
n = q + 12
Now we can solve this system of equations. By substituting n from the second equation into the first, we get:
5(q + 12) + 25q = 210
Solving for q we find:
5q + 60 + 25q = 210
5q + 25q = 210 - 60
30q = 150
q = 5
Now we substitute the value of q into n = q + 12 to find the number of nickels:
n = 5 + 12
n = 17
Liliana has 5 quarters and 17 nickels in her backpack.