martas math textbook weighs $\frac{4}{5}$ of a pound less than 4 times the weight of the book she is reading…

martas math textbook weighs $\frac{4}{5}$ of a pound less than 4 times the weight of the book she is reading for her language arts class. if the weight of the math textbook is $2\frac{1}{5}$ pounds, which shows the correct equation and value of $x$, the weight of martas book for language arts?\n$4x + \frac{4}{5}=2\frac{1}{5};x = \frac{7}{20}$ of a pound\n$4x-\frac{4}{5}=2\frac{1}{5};x=\frac{3}{4}$ of a pound\n$4x+\frac{4}{5}=2\frac{1}{5};x=\frac{3}{4}$ of a pound\n$4x - \frac{4}{5}=2\frac{1}{5};x=\frac{7}{20}$ of a pound

martas math textbook weighs $\frac{4}{5}$ of a pound less than 4 times the weight of the book she is reading for her language arts class. if the weight of the math textbook is $2\frac{1}{5}$ pounds, which shows the correct equation and value of $x$, the weight of martas book for language arts?\n$4x + \frac{4}{5}=2\frac{1}{5};x = \frac{7}{20}$ of a pound\n$4x-\frac{4}{5}=2\frac{1}{5};x=\frac{3}{4}$ of a pound\n$4x+\frac{4}{5}=2\frac{1}{5};x=\frac{3}{4}$ of a pound\n$4x - \frac{4}{5}=2\frac{1}{5};x=\frac{7}{20}$ of a pound

Answer

Explanation:

Step1: Translate the problem into an equation

Let $x$ be the weight of the language - arts book. The math textbook weighs $\frac{4}{5}$ of a pound less than 4 times the weight of the language - arts book. So the equation is $4x-\frac{4}{5}=2\frac{1}{5}$.

Step2: Convert the mixed - number to an improper fraction

$2\frac{1}{5}=\frac{2\times5 + 1}{5}=\frac{11}{5}$. The equation becomes $4x-\frac{4}{5}=\frac{11}{5}$.

Step3: Add $\frac{4}{5}$ to both sides of the equation

$4x=\frac{11}{5}+\frac{4}{5}$. Since $\frac{11}{5}+\frac{4}{5}=\frac{11 + 4}{5}=\frac{15}{5}=3$, we have $4x = 3$.

Step4: Solve for $x$

Divide both sides of the equation $4x = 3$ by 4, so $x=\frac{3}{4}$.

Answer:

B. $4x-\frac{4}{5}=2\frac{1}{5};x = \frac{3}{4}$ of a pound