The sum of two hopeful numbers is 151. The lesser number is 19 much more than the sqr root of the higher number. What is the value of the difference between greater and also the lesser number?

The answer united state 91 however i keep getting 137, since when ns solved, the better number to be 144 and the smaller sized was 7.

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How is the prize 91? Thanks.

The square root of 144 is 12. 19 an ext than 12 is 31. 144+31 does no equal 151.

Try the following smallest perfect square, the square root of 121 is 11, 19 an ext than 11 is 30. 30+121 does same 151. The distinction of 121 and also 30 is 91.

x=y=151

sqrt(x)+19=y

This is one wherein you really need to test the answers due to the fact that it would certainly be a ache to settle for x and also y.

Start through H

x+y=151

x-y=85

using elimination

2x=236

x=118

118 is not a perfect square

F,G, and also K will certainly all be ruled the end for the exact same reason.

try J

x+y=151

x-y=91

2x=242

x=121

sqrt(x)=11

11+19=30

30+121=151

It's J

x+y=151

sqrt(x)+19=y

This is one wherein you really should test the answers since it would be a pains to settle for x and y.

It's not *too* negative to solve for x and y. Flip the an initial equation roughly so the y=151-x, and also then plug that into the 2nd equation:

sqrt(x)+19=151-x

x+sqrt(x)-132=0

Then you just need come find determinants of -132 that include up come 1 (ok, looking in ~ the answers could aid with that), and also factor it together a polynomial: (sqrt(x)-11)(sqrt(x)+12)=0. Therefore sqrt(x) is one of two people 11 or -12 (but really simply 11 due to the fact that they claimed it was positive). Climate x is 121, leaving y to it is in 30.

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