Question

Please help i will fan and medal!!!


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

@xGuardians

Answer 2

(t - 6) / 6 = y then (t + 7)/7 = y
Set them equal to each other
(t-6)/6 = (t+7)/7
Find LCM.

Answer 3

42?

Answer 4

Yes, so multiply both sides by 42

Answer 5

wait what

Answer 6

So on the left, you get 42/6 = 7
Therefore you do 7(t-6)

Answer 7

let's check

malin's expression would be:
\[\frac{ t -6 }{ 6 }\]

shawn's expression would be:
\[\frac{ t + 7 }{ 7 }\]

since the number (t) is the same, we can set it equal to each other \[\frac{ t - 6 }{ 6 } = \frac{ t + 7 }{ 7 }\]

cross multiply:
\(7(t-6) = 6(t+7)\)

solve for t
\(7t - 42 = 6t + 42\)

\(t = 84\)

Answer 8

Multiply then simplify.

Answer 9

nvmind i got it

Answer 10

@calculusxy is faster, but when you get to rational denominators, using the LCM is easier to understand.

Answer 11

ok.

Answer 12

can you help me with another one?

Answer 13

This season, Lisa's lacrosse team has won 2/3 of their home games (games played at Lisa's school), but just 2/5 of their away games (games played at other schools). In total, Lisa's team has won 26 games out of 49 games they have played. How many home games has Lisa's team played?

Explain how you solved the problem.