Question

Let us assume we have two numbers. x is small number and y is large
number. 4 times the x is less then 3 times the y by 5. If sum of (x and y)
is greater then 6 times the difference of (x and y) by 6. What is the value
of x and y?

Answer 1

Given:

Let us assume we have two numbers. x is a small number and y is a large  number. 4 times the x is less than 3 times the y by 5. If the sum of (x and y)  is greater than 6 times the difference of (x and y) by 6.

To Find:

What is the value  of x and y?

Solution:

First, we will need to frame a linear equation with two variables x and y, the first condition is given as 4 times the x is less than 3 times y by 5 which can be framed as,

3y-4x=5      -(1)

And the second condition is given as the sum of (x and y)  is greater than 6 times the difference of (x and y) by 6 which can be framed as

6(x+y)-(x-y)=6

7y+5x=6       -(2)

Now we will solve these two equations by multiplying the first equation by 5 and the second equation by 4 and then adding both the equations,

5(3y-4x)+4(7y+5x)=25+24

43y=49

y=49/43

Now substituting values of y in equation 1 to find the value of x we have,

$3*\frac{49}{43} -4x=5\\x=\frac{-17}{43}$

Hence, the value of x and y is -17/43 and 49/43 respectively.

Answer 2

Value of x = 43 and y = 59

Given:

• Two numbers
• x is small number and y is large number
• 4 times the x is less then 3 times the y by 5
• sum of (x and y) is greater then 6 times the difference of (x and y) by 6

To Find:

• Value of x and y

Solution:

Step 1:

Create first equation using 4 times the x is less then 3 times the y by 5

4x = 3y - 5

=> 4x - 3y  = -5  Eq1

Step 2:

Create second equation using sum of (x and y) is greater then 6 times the difference of (x and y) by 6 and simplify

x + y = 6(y - x) + 6         ( y - x taken as y is larger)

x + y = 6y - 6x + 6

=> 7x - 5y  = 6    Eq2

Step 3:

5 * Eq1 - 3 * Eq2 and solve for x

20x - 15y  -21x +15y  = -25 - 18

=> -x = -43

=> x = 43

Step 4:

Substitute x= 43 in Eq1  and solve for y

=> 4(43) - 3y  = -5

=> 172 - 3y = -5

=> -3y = -177

=> y = 49

Value of x = 43 and y = 59