Question

QUADRATIC EQUATION – WORD PROBLEMS

Fatima got 16 marks more than Zahra in Math test. The product of their mark is 1380. Find their marks.

The answer 30 ,46
I just need the steps

Answer 1

Fatima's points = 46

Zahra's points = 30

Explanation:

Let's give names to the unknowns (the number of points each one got)

Fatima's points = y

Zahra's points = x

Now create the equations given by the info they provide:

"Fatima got 16 marks more than Zahra"

y = x + 16

"The product of their mark is 1380."

x * y = 1380

Now use the first equation as substitution for "y" in the second equation:

x * (x + 16) = 1380

reduce the expression:

x^2 + 16 x = 1380

x^2 + 16 x - 1380= 0

Solve using quadratic formula:

`x=(-16+/- √(16^2+4(1380)) )/(2) \\x=(-16+/- √(5776) )/(2) \\x=-8+/- 38\\x = 30\,\,\,or\,\,\,x=-46`

we pick 30 since the scores from a test must be larger than zero.

Now we use the first equation to solve for the other variable;

y = 30 + 16 = 46

then x = 30 and y = 46