in a class test, the sum of shefali's marks in mathematics and english is 30. had she got 2 marks more in mathematics and 3 marks less in english, the product of the marks would be 210. find the marks
Answers
Answer :
Let Shefali's marks in mathematics be = x
Let Shefali's marks in english be = y
given that - x + y = 30
x = 30-y ------ (1)
(x+2) * (y-3) = 210 ------(2)
substituting 1 in 2
(30-y+2) * (y-3) = 210
(32-y) * (y-3) =210
32y - 96 - y² +3y - 210 = 0
35y - y² - 306 = 0
y² - 35y + 306 = 0
now we can solve this quadratic equation by quadratic formula
x= -b±√b²- 4 ac ÷ 2a
a= 1 ,b= -35 , c=306
x= - (-35)±√35²- 4*(1)*(306) ÷ 2*(1)
x= 35 ±√1225-1224 ÷ 2
x= 35 ± 1 ÷2
x = 35 + 1 ÷2 or x = 35 - 1 ÷2
x = 36÷2 or x = 34÷2
x= 18 or x = 17
so .... 30 - 18 = 12
or
30 - 17 = 13
marks in marks in mathematics = 12 , marks in english = 18
or
marks in mathematics = 13 , marks in english = 17
hope, it was helpful
Let the marks of maths = x
Let the marks of english=30-x
━━━━━━━━━━━━━━━
(x+2)(30-x-3)=210
(x+2)(27-x)=210
27x-+54-2x=210
+27x-2x+54-210=0
+25x-156)=0
-25x+156=0
-25x+156=0
-13x-12x+156=0
x(x-13) -12(x-13) =0
(x-12) (x-13) =0
━━━━━━━━━━━━━━━
x-12=0
x=12
x-13=0
x=13
━━━━━━━━━━━━━━━
Shefali got marks in maths = 12
Shefali got marks in English= 30-12=18
OR
Marks in maths = 13
Marks in English= 30-13=17