Quadratic equation Word problem

"The denominator of a fraction is greater than its numerator by 5."

If the numerator = n, then the denominator = n+5.

setting up a problem usually is a series of challenges and this one this one has three deduction challenges and one math skill challenge

try this

part 1 (deduction challenge)

I've got a fraction (p/q) and the denominator q is five more than the numerator. so q+5=p, and the fraction is [p/(p+5)]

part 2 (deduction challenge)

Now I've got another fraction (r/s ) and the numerator and denominator are one less than the numerator and denominator the first fraction. So r=p-1, and s=q-1=(p+5)-1=p+4. So (r/s)=[(p-1)/(p+4)]

part 3 (deduction challenge)

the difference between the first fraction and the second is a fraction (5/42). Difference implies a subtraction and since it is a reduction when going from the first fraction to the second this leads to subtracting the first fraction [p/(p+5)] from the second [(p-1)/(p+4)] results in (5/42) being left over, or

[p/(p+5)]-[(p-1)/(p+4)]=(5/42)

part 4--(math skill challenge)

I really don't consider this part of the deductive problem as this is just manipulation. In reality the problem is already solved---it is just messy.

So this challenge is really a cleaning operation, using math skills that you already know.

Note there I used the variable (p) in this relation (instead of n) but this can be rearrange into a polynomial of the same form with the same factors when you multiply the denominators through by common fractions [in this case the common fraction --numerator is 42(p+5)(p+4)].

Nevertheless when you do the crunch you'll get the desired polynomial.

Rap