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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