Problem Solving

AAPL wrote:Mrs. Jones divided $120 evenly among her children. Tom, the eldest, decided to give each of his brothers and sisters $6 of his share. Eventually, Tom ended up with $12. How many children does Mrs. Jones?

A. 4
B. 5
C. 6
D. 8
E. 10

Let x = # children that Mrs. Jones has
This means x-1 = # of Tom's siblings.
If Tom gives each sibling $6, the total amount that Tom gave to siblings = 6(x - 1)
AFTER giving $6 to each sibling, Tom had $12 remaining.
So, BEFORE he gave away the money, the amount Tom had = 12 + 6(x - 1) = 12 + 6x - 6 = 6x + 6

Since each child originally received the SAME amount, we know that EACH child received 6x + 6 dollars
Since there are x children, the TOTAL amount the children received = (x)(6x + 6)
Since the x children received a TOTAL of $120, we can write: (x)(6x + 6) = 120
Expand equation: 6x² + 6x = 120
Subtract 120 from both sides: 6x² + 6x - 120 = 0
Divide both sides by 6 to get: x² + x - 20 = 0
Factor to get: (x + 5)(x - 4) = 0
So, EITHER x = -5 OR x = 4
Since x cannot be negative, we can rule out x = -5, which means x must equal 4

Answer: A

Cheers,
Brent

AAPL wrote:Mrs. Jones divided $120 evenly among her children. Tom, the eldest, decided to give each of his brothers and sisters $6 of his share. Eventually, Tom ended up with $12. How many children does Mrs. Jones?

A. 4
B. 5
C. 6
D. 8
E. 10

Let x = the number of children Mrs. Jones has. Since Tom is one of the children, he has (x - 1) siblings. Tom receives 120/x dollars and he gives 6 dollars to each of his (x - 1) siblings and he has 12 dollars left.

We can create the equation:

120/x - 6(x - 1) = 12

120 - 6x(x - 1) = 12x

120 - 6x^2 + 6x = 12x

-6x^2 - 6x + 120 = 0

Dividing both sides by -6, we have:

x^2 + x - 20 = 0

(x + 5)(x - 4) = 0

x = -5 or x = 4

Since x can't be negative, x must be 4.

Answer: A