Problem of the Week

Updated at Oct 20, 2025 12:31 PM

For this week we've brought you this equation problem.

How would you solve the equation \(\frac{5}{4n}-4(3-n)=\frac{69}{16}\)?

Here are the steps:



\[\frac{5}{4n}-4(3-n)=\frac{69}{16}\]

1
Multiply both sides by \(16n\).
\[20-64n(3-n)=69n\]

2
Simplify.
\[20-192n+64{n}^{2}=69n\]

3
Move all terms to one side.
\[20-192n+64{n}^{2}-69n=0\]

4
Simplify  \(20-192n+64{n}^{2}-69n\)  to  \(20-261n+64{n}^{2}\).
\[20-261n+64{n}^{2}=0\]

5
Split the second term in \(20-261n+64{n}^{2}\) into two terms.
\[64{n}^{2}-5n-256n+20=0\]

6
Factor out common terms in the first two terms, then in the last two terms.
\[n(64n-5)-4(64n-5)=0\]

7
Factor out the common term \(64n-5\).
\[(64n-5)(n-4)=0\]

8
Solve for \(n\).
\[n=\frac{5}{64},4\]

Done

Decimal Form: 0.078125, 4
Cymath foriOSAndroid