SOLUTION: Carlos scored 15 more points than John in the baseball game. If the product if the two point totals is 154, how many points did each boy score?

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Question 40560: Carlos scored 15 more points than John in the baseball game. If the product if the two point totals is 154, how many points did each boy score?
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Carlos scored 15 more points than John in the baseball game. If the product if the two point totals is 154, how many points did each boy score?
Let number of John points be "x"
The number of Carlos points is "x+15"
EQUATION:
x(x+15)=154
x^2+15x-154=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B15x%2B-154+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%2815%29%5E2-4%2A1%2A-154=841.

Discriminant d=841 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-15%2B-sqrt%28+841+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2815%29%2Bsqrt%28+841+%29%29%2F2%5C1+=+7
x%5B2%5D+=+%28-%2815%29-sqrt%28+841+%29%29%2F2%5C1+=+-22

Quadratic expression 1x%5E2%2B15x%2B-154 can be factored:
1x%5E2%2B15x%2B-154+=+1%28x-7%29%2A%28x--22%29
Again, the answer is: 7, -22. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B15%2Ax%2B-154+%29

Hope this helps.
Cheers,
Stan H.