Q44. - Algebra 1

Question

Tim’s bank contains quarters, dimes, and nickels. He has 3 more dimes than quarters and 6 fewer nickels than quarters and the total coins is 63.

Write and solve the equation to find how many quarters Tim has.

Step-by-Step Solution

Answer

The number of quarters is 22.

Step 1. Given information.

Tim’s bank contains quarters, dimes, and nickels. He has 3 more dimes than quarters and 6 fewer nickels than quarters.

Total coins = 63

Step 2. Mention the variables.

Consider the number of quarters be q, the number of dimes is d and the number of nickels is n.

So, from the given information:

$q+d+n=63$

Step 3. Write the equation.

Since Tim’s bank contains 3 more dimes than quarters.

So,

$q+3=d$

Again, Tim’s bank 6 fewer nickels than quarters.

So,

$q-6=n$

Step 4. Solve equations.

Substitute $d=q+3$ and $n=q-6$ in the equation $q+d+n=63$.

 $$\begin{gathered} q+d+n=63 \\ q+q+3+q-6=63 \\ 3q=63+3 \end{gathered}$$

Solve this equation in below.

$$\begin{gathered} 3q=66 \\ q=\frac{66}{3} \\ q=22 \end{gathered}$$