24 more than the quotient of b and 2 is 8.  Solve for b. 

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tjbrewer's profile pic

tjbrewer | Elementary School Teacher | (Level 2) Associate Educator

Posted on

The quotient of b and 2 is a little ambiguous because division does not have a commutative property.  `b-:2!=2-:b` I will solve it for each possibility. 

The order of b and 2 implies that the quotient is the quotient of `b-:2` We are told that 24 more than that quotient is 8.  From this clue we can formulate the following number sentence:
`(b-:2)+24=8` We subtract 24 from each side of the equation and we get `b-:2=-16` We multiply each side by 2 and we find b=-32. 

If they meant the quotient of `2-:b` then our number sentence is:
`(2-:b)+24=8` Again we subtract 24 from each side to get `2-:b=-16` We multiply each side by b and we get `2=-16b` We divide both sides by -16 and `b=-1/8`

The first solution is more likely but both fit the question. 

steveschoen's profile pic

steveschoen | College Teacher | (Level 1) Associate Educator

Posted on

Translating the statement into a math equation, we have:

(b/2) + 24 = 8

So, we would subtract 24 from each side

b/2 = -16

Then, multiply by 2

b = -32

michuraisin's profile pic

michuraisin | Student, College Junior | (Level 1) Salutatorian

Posted on

The quotient is the number one gets when one number is divided by another number. What makes your question a little unclear is that I don't know if the quotient is b/2 or 2/b.

If we're looking at b/2, then the question could be solved like this:

(b/2)+24=8

(b/2)+24-24=8-24

b/2=-16

(b/2)*2=-16*2

b=-32

With the other scenario of 2/b, then the answer would be solved in this way:

(2/b)+24=8

(2/b)+24-24=8-24

2/b=-16

(2/b)(b)=-16b

2=-16b

2/-16=-16b/-16

-1/8=b

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