SOLUTION: a boy buys x eggs at (x-8) cents each and (x-2) rashers of bacon at (x-3) cents each. if the total bill is $1.75, how many eggs does he buy?

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: a boy buys x eggs at (x-8) cents each and (x-2) rashers of bacon at (x-3) cents each. if the total bill is $1.75, how many eggs does he buy?      Log On


   

Question 180850: a boy buys x eggs at (x-8) cents each and (x-2) rashers of bacon at (x-3) cents each. if the total bill is $1.75, how many eggs does he buy?
Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
x(x-8)+(x-2)(x-3)=175
x^2-8x+x^2-5x+6=175
2x^2-13x-169=0
x=13
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Ed
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Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 2x%5E2%2B-13x%2B-169+=+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=%28-13%29%5E2-4%2A2%2A-169=1521.

Discriminant d=1521 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--13%2B-sqrt%28+1521+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-13%29%2Bsqrt%28+1521+%29%29%2F2%5C2+=+13
x%5B2%5D+=+%28-%28-13%29-sqrt%28+1521+%29%29%2F2%5C2+=+-6.5

Quadratic expression 2x%5E2%2B-13x%2B-169 can be factored:
2x%5E2%2B-13x%2B-169+=+%28x-13%29%2A%28x--6.5%29
Again, the answer is: 13, -6.5. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B-13%2Ax%2B-169+%29