The sum of two integers is 704 and the larger number is 11 more than 8 times the smaller number.Find the two integers.

The sum of two integers is 704 and the larger number is 11 more than 8 times the smaller number. Find the two integers.

Detailed Solution:

Let us say that the two integers are X and Y.

Let X be greater than Y.

Given that the sum of the two integers is 704.

Therefore the first  equation would be

X+Y=704—–> Equation 1

We are also given that the larger number is 11 more than 8 times the smaller number.

Hence the  equation corresponding to this sentence would be

X=8X +11—–>Equation 2

Solving Equations:

X+Y=704—> Equation 1

X=8Y +11—>Equation 2

From Equation 1,  Y=704-X

Substituting the value  of Y =704-x in the  equation 2.

X= 8( 704-X)+11

X=5632-8X+11

9X=5643

X=627

Therefore the  value of y = 704-X=704-627

Y=77

Verification:

We can cross-check the answers we got.

Let us plug the values of  X and  Y in the first equations to check whether they hold good.

X+Y =704

627+77=704

704=704

Therefore the  X and  Y values we found work good for the  equation1.

Let us plug the values of  X and  Y in the second equations

X=8Y +11

627=8*77+11

627=616+11

627=627

Therefore the  X and  Y values we found work good for equation 2.

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