In class test, the sum of Shefali's marks in math's and english is 30. Had she got 2 marks more in math's and 3 marks less in english, the product of their marks would have been 210. Find her marks in the two subjects.
Answers
Answer:
Marks in Maths = 18, English = 17
Step-By-Step explanation:
• Let us assume that the marks in Maths be "x" and the Marks in English be "30-x".
According to the given question :
• We must find the value of x first and subtract the value of x with 30 and (30-x).
Step 1:
• Since the question is based on the quadratic equations chapter, We must represent the following question into a Quadratic equation.
→ (x + 2) (x - x - 3) = 210.
Step 2:
• Now, multiplying (x with 27), (x with x) and (2 with 27) and (2 with x) , we get:
→ (x + 2) (27 - x) = 210.
→ 27x - x² + 54 - 2x = 210.
Step 3:
• Taking 210 to LHS (Left hand side) , It will become negative.
→ 27x - x² + 54 - 2x - 210 = 0.
→ -x² + 25x + 54 - 210 = 0.
→ -x² + 25x - 210 = 0.
→ x² - 25x + 156 = 0.
Further solving, now we got required quadratic form:
• From above answer steps:
- a = 1.
- b = -25.
- c = 156.
Multiplying the value of "a with c" we get:
→ 1 × 156 = 156, Then find factors of 156 are:
We need to get the value of b by subtracting the factors of 156.
→ -12 - 13 = -25, here we go. This is the value of "b" in our required steps above. We are just going to replace it with the value we got subtracting factors of 156.
To verify:
→ -12 (-13) = 156 (Value of C).
Applying the values in our new equation, we get:
→ x² - (-12 - 13)x + 156 = 0.
→ x² - 12x - 13x + 156 = 0
Now, talking common from above step:
→ x (x - 12) - 13 (x-12) = 0, here we got value x - 12 after talking common, we know that -13 (-12) is 156.
Talking common again:
→ (x - 13) = 0 , (x - 12) = 0.
Talking values to the other sides:
→ x = 13 , x = 12, here, since the numbers are transferred to the other side we have positive numbers.
Using the above values:
→ 30 - 12.
→ 18.
→ 30 - 13.
→ 17.
Hence, Shefali's marks in Mathematics is 18, Marks in English is 17.