Maths Help Equations

[cshelmo]

how would i turn this:

e) (n-2)((48/n) + 3) - 48 = 22

into the standard form of a quadratic equation?

using that quadratic equation how would i solve for the following:

1. how many mugs were purchased?
2. what was the original cost per mug?
3. what profit was made on wach mug?
4. when solving a quadratic equation, there are normally two solutions,
why were you able to discard one of the solutions in this case?

[scotstone]

If (n-2)(48/n+3) - 48 = 22 then expanding brackets:-

48 - 96/n + 3n - 6 - 48 = 22 and rearranging

3n - 96/n - 28 = 0 and multiplying through by n gives

3n^2 - 28n - 96 = 0 which is the standard form of a Q.E.

Factorising to (3n + 8)(n - 12) = 0 therefore:-

n = - 8/3 or 12

Assuming n = number of mugs which cannot be a negative number then n = 12 . The equation gives the total profit made ie �22 when 12 mugs were bought and 10 sold ie(n - 2) . The second bracket gives the price paid ie. �48 for the 12 mugs at �4 each and a profit of �3 added on each ie (48/n + 3) and if the cost price of �48 is deducted this leaves a profit of �22.