i think of a number. if i divide the sum of 6 and the number by 3, the result is 4 more than one quarter of the number. find the number

-12

Step-by-step explanation:

Let the number be A

Given if you divide the sum of six and the number A by 3, the result is 4 more than 1/4 of A

That's

6+A/3 = 4+1/4 of A

6+A/3 = 4+1/4 x A

6+A/3 = 4+A/4

Cross multiply

4 (6 + A) = 3 (4 + A)

Distribute

4 x 6 + 4 x A = 3 x 4 + 3 x A

24 + 4A = 12 + 3A

Subtract 24 from both sides to eliminate 24 on the left side

24 - 24 + 4A = 12 - 24 + 3A

4A = - 12 + 3A

Subtract 3A from both sides so the unknown can be on one side

4A - 3A = - 12 + 3A - 3A

A = - 12

Check

6 + (-12) / 3 = 4 + (-12) / 4

6 - 12/3 = 4 - 12/4

-6/3 = - 8/4

-2 = - 2