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SAT Exam  >  SAT Questions  >  The sum of two positive numbers is 14 and dif... Start Learning for Free
The sum of two positive numbers is 14 and difference between their squares is 56. What is the sum of their squares?
  • a)
    106
  • b)
    196
  • c)
    53
  • d)
    68
Correct answer is option 'A'. Can you explain this answer?
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The sum of two positive numbers is 14 and difference between their squ...
The sum of two positive number is 14 and difference between their square is 56. what is the sum of their square
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The sum of two positive numbers is 14 and difference between their squ...
The Problem:
We are given two positive numbers such that their sum is 14 and the difference between their squares is 56. We need to find the sum of their squares.

Step-by-Step Solution:

Let's assume the two positive numbers as "x" and "y".

1. Formulating the Given Information:
From the problem statement, we can translate the given information into mathematical equations:

- The sum of the two numbers is 14: x + y = 14
- The difference between their squares is 56: x^2 - y^2 = 56

2. Simplifying the First Equation:
We can solve the first equation for one of the variables and substitute it into the second equation to find the value of the other variable.

From the first equation: x = 14 - y

3. Substituting into the Second Equation:
Substituting the value of "x" from step 2 into the second equation, we have:

(14 - y)^2 - y^2 = 56

4. Expanding and Simplifying the Second Equation:
Expanding the equation, we get:

196 - 28y + y^2 - y^2 = 56

Simplifying further, the y^2 terms cancel out:

196 - 28y = 56

5. Solving for "y":
Rearranging the equation, we get:

28y = 196 - 56
28y = 140
y = 140/28
y = 5

6. Substituting "y" into the First Equation:
Substituting the value of "y" into the first equation, we have:

x + 5 = 14
x = 14 - 5
x = 9

7. Finding the Sum of their Squares:
We need to find the sum of their squares, which is x^2 + y^2:

Sum of squares = 9^2 + 5^2 = 81 + 25 = 106

Therefore, the correct answer is option A) 106.
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The sum of two positive numbers is 14 and difference between their squares is 56. What is the sum of their squares?a)106b)196c)53d)68Correct answer is option 'A'. Can you explain this answer?
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