Solve the following equations with fractions.
$\frac{2}{5}y-3=\frac{1}{4}$

• A. $y=\frac{65}{8}$
• B. $x=520$
• C. $y=-\frac{55}{8}$
• D. $x=440$

Answer: (A)

Verified step by step guidance

1. Start with the given equation: \(\frac{2}{5}y - 3 = \frac{1}{4}\).
2. The goal is to isolate the variable \(y\). First, add 3 to both sides of the equation to move the constant term to the right side: \(\frac{2}{5}y = \frac{1}{4} + 3\).
3. Convert the whole number 3 to a fraction with denominator 4 to combine the terms on the right side: \(3 = \frac{12}{4}\), so \(\frac{1}{4} + 3 = \frac{1}{4} + \frac{12}{4}\).
4. Add the fractions on the right side: \(\frac{1}{4} + \frac{12}{4} = \frac{13}{4}\), so now the equation is \(\frac{2}{5}y = \frac{13}{4}\).
5. To solve for \(y\), multiply both sides of the equation by the reciprocal of \(\frac{2}{5}\), which is \(\frac{5}{2}\): \(y = \frac{13}{4} \times \frac{5}{2}\). This will give you \(y\) isolated.