Question

Liliana has $\$2.10$ in nickels and quarters in her backpack. She has $12$ more nickels than quarters. How many coins of each type does she have?

Short answer

Liliana has $17$nickels and $5$quarters in her backpack.

Step-by-step solution

Step 1. Given information.

Consider the given question,

Liliana has $12$more nickels than quarters.

We know, the value of a nickels is localid="1647109290873" $\$0.05$and the value of quarters is localid="1647109292642" $\$0.25$. The total value of all the coins is localid="1647109294933" $\$2.10$.

Assume nand qto be the number of nickels and quarters.

localid="1647109297681" $q=n-12$

Make the table,

Step 2. Form the equation.

Consider the table, we can see,

$$\begin{gathered} 0.25\left(n-12\right)+0.05n=2.10 \\ 0.25n-3+0.05n=2.1 \\ 0.3n=5.1 \\ n=17 \end{gathered}$$

Then,

$$\begin{gathered} q=17-12 \\ q=5 \end{gathered}$$

Therefore, the number of nickels is $17$and the number of quarters is$5$.