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How do you solve for $t$ in $a = p + prt?$

Last updated date: 14th Jul 2024
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Hint: As we know that the above given equation $a = p + prt$ is a linear equation. An equation for a straight line is called a linear equation. The standard form of linear equations in two variables is $Ax + By = C$ . When an equation is given in this form it’s also pretty easy to find both intercepts $(x,y)$. By transferring the positive $a$ to the right hand side value gives the required solution.

Complete step by step solution:
As we know that the above given equation is a linear equation and to solve for $t$ we need to isolate the term containing $t$ on the left hand side i.e. to simplify $a = p + prt$ and solving for variable $t$ , move all the terms containing $p,r$ to the right.
Here we will transfer the $ + p$ to the right hand side and we get $a - p = prt$.
Now since both $p$ and $r$ are being multiplied in left hand side, so when we will transfer it to the right hand side it will turn into division: $\dfrac{{a - p}}{{pr}} = t$. It can also be written as
$\dfrac{a}{{pr}} - \dfrac{p}{{pr}} = t$.
Hence the required value of $t$ is $\dfrac{{a - p}}{{pr}}$.

Note: We should keep in mind the positive and negative signs while calculating the value of any variable as it will change it’s slope and value. In the equation $Ax + By = C$ ,$A$ and $B$are real numbers and $C$ is a constant, it can be equal to zero$(0)$ also. These types of equations are of first order. Linear equations are also first-degree equations as it has the highest exponent of variables as $1$ . The slope intercept form of a linear equation is $y = mx + c$ ,where $m$ is the slope of the line and $b$ in the equation is the y-intercept and $x$ and $y$ are the coordinates of x- axis and y-axis , respectively.