Question

Malin and Shawn begin with the same number, t. Malin subtracts 6 from t and then divides the result by 6. Shawn adds 7 to t and then divides the result by 7. If Malin's final answer is the same as Shawn's final answer, what was the number t?

Answer 1

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, $13$.)

Answer 2

T

adds 6
t-6

divides by 6
(t-6)/6



shawn
7+t

divide by 7
(7+t)/7


theyare equal


(t-6)/6=(7+t)/7
times 42 both sides
7(t-6)=6(t+7)
distribute
7t-42=6t+42
minus 6t both sides
t-42=42
add 42 both sides
t=84