Question 620161: JAMES, ASHLEY, AND NICOLE, ALL SIBLINGS VISITING SCENE75, HAVE COLLECTIVELY WON A TOTAL OF 340 REDEMPTION PRIZE POINTS. THEIR MOTHER, KATHY, DECIDES HOW THE POINTS WILL BE SPLIT AMONGST THE THREE CHILDREN. SHE SAYS THAT JAMES AND ASHLEY BOTH BEHAVED VERY POORLY TODAY, THOUGH JAMES BEHAVED EVEN WORSE THAN ASHLEY. KATHY ASKS YOU TO SPLIT THE POINTS SUCH THAT JAMES RECEIVES 40 POINTS FEWER THAN ASHLEY AND THAT ASHLEY RECEIVES 80 POUNTS FEWER THAN NICOLE. HOW MANY POINTS DOES EACH CHILD RECEIVE?
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! Let J equal the number of points that James gets, A equal the number of points that Ashley gets, and N equal the number of points that Nicole gets.
.
The sum of all the points is 340. Therefore, we can write the equation:
.
J + A + N = 340
.
But we are told that the number of points that James gets is 40 less than the number of points Ashley gets. So if we take 40 points from Ashley the result equals the number of points for James. In equation form this says:
.
J = A - 40
.
This tells us that in our equation for the total number of points we can replace J with A - 40 because they are equal. So we substitute A - 40 for J and the equation for the total number of points becomes:
.
(A - 40) + A + N = 340
.
Next we are told that the number of points that Ashley gets is 80 less than the number of points Nicole gets. So if we take 80 points from Nicole, the result is the number of points for Ashley. In equation form this is:
.
A = N - 80
.
This means that we can replace every A in our equation with N - 80 because they are equal. So let's do that and our equation then is:
.
((N - 80) - 40) + (N - 80) + N = 340
.
Since all the sets of parentheses are preceded by plus signs, we can just remove the parentheses without changing the signs of the terms they contain. Removing the parentheses results in:
.
N - 80 - 40 + N - 80 + N = 340
.
The constants on the left side are -80, -40, and -80. When we add these we get -200 and our equation becomes:
.
N + N + N - 200 = 340
,
Combine the three N terms to make our equation:
.
3N - 200 = 340
.
Get rid of the -200 on the left side by adding 200 to both sides. This results in:
.
3N = 540
.
Finally, solve for N, the number of points Nicole gets, by dividing both sides by 3 and we get:
.
N = 180
.
Ashley gets 80 points less than Nicole, so Ashley gets 100 points, and James gets 40 points less than Ashley, so he gets 60 points.
.
That's the solution. James = 60, Ashley = 100, and Nicole = 180 points.
.
To check this answer, we just add the three scores (60, 100, and 180) and ensure that the total is 340 points. It is, so our answer is correct.
.
Hope this helps you to understand the problem.
.
|
|
|
