Question

Sum of two numbers is 17 and the difference between their squares is 68. Determine the product of the numbers.
A) 62.85
B) 72.75
C) 92.75
D) 68.25​

Answer 1

Answer:

4) 68.25

Step-by-step explanation:

a+b=17

(a+b)(a-b)=68

a-b=4

so by simultaneous equations, a=10.5,b=6.5

multiply a and b , u will get 68.25

Answer 2

Given:

The sum of the two numbers is 17 and the difference between their squares is 68.

To find:

The product of the numbers.

Solution:

The correct option is D) 68.25.

To answer this question, we will follow the following steps:

Let the two numbers be x and y.

Now, according to the question,

The sum of two numbers = 17

So,

$x + y = 17 \: \: (i)$

Also,

The difference between their squares = 68

This means,

${x}^{2} - {y}^{2} = 68$

From algebraic identities, the above can be written as

$(x + y)(x - y) = 68$

$(17)(x - y) = 68$

[from (i)]

$x - y = 4 \: \: (ii)$

Adding (i) and (ii), we get

$2x = 21$

$x = 10.5$

On putting the value of x in (i), we get

$y = 6.5$

Now,

The product of x and y

$= 10.5 \times 6.5$

$= 68.25$

Hence, the product of the numbers is D) 68.25