a. I will represent the number as x.
b. Since they had equal amounts, it is 25000
x
c. It is 25000
x+25
d. 25000 = 25000 + 50
x x+25
This is the mathematical sentence, if you mean standard quadratic equation we first simplify:
25000 = 25000+50x+1250
x x+25
25000 = 26250+50x
x x+25
We cross-multiply,
25000(x+25) = x(26250+50x)
We divide the equation by 50.
500(x+25)=x(525+x)
500x+12500=525x+x²
0=x²+25x-12500 This is the standard form but I will further simplify it,
Method 1: Guess and Check
We look for two numbers with a product of 12500 and a difference of 25,
250 - 50 = 200 X
125 - 100 = 25 √
Therefore it is 0 = (x+125)(x-100), this means x=-125 or x=100.
Method 2: Quadratic formula
x = -25 ± √(25²+50000) = -25 ± √50625 = -25 ± 225 = -125 or 100
2 2 2