Answer:
t=84
Step-by-step explanation:
Malin's answer is $\frac{t-6}{6}$. Shawn's answer is $\frac{t+7}{7}$. We know these are equal, so we have the equation
$\frac{t-6}{6} = \frac{t+7}{7}.$
To eliminate denominators from the problem, we multiply both sides by $6\cdot 7$:
$\frac{6\cdot 7\cdot (t-6)}{6} = \frac{6\cdot 7\cdot (t+7)}{7},$
then simplify to get
$7\cdot (t-6) = 6\cdot (t+7).$
The parentheses are important here! For example, the parentheses on the left side of the equation tell us that it is $t-6$, not just $t$, which is multiplied by $7$.
Now we expand using the distributive property:
7t - 7\cdot 6 &= 6t + 6\cdot 7;\\
7t - 42 &= 6t + 42.
Adding $42$ to both sides gives
$7t = 6t + 84,$
then subtracting $6t$ from both sides gives $t=\boxed{84}$.
(We can check that starting from $t=84$, Malin and Shawn do indeed get the same final answer -- namely, $13$.)
