If there is 80 total households, couldn’t you do:

S=30-B

Y=39

30-B+39+11=80

What am I missing?

Idk about the first option, but the second option is wrong right?

30 + 46 + 11 > 80

From my understanding not necessarily, because it does not specify only swimming pool or only yard, so I’m assuming its total:

S=30-B

Y=46-B

30-B+46-B+11=80

30+46+11-2B=80

87-2B=80

-2B=-7

B=3.5

It gives you a decimal but if the numbers were different it would be able to provide you an answer?

omg

Assuming S means only pool and Y means only yard, I believe your equation is saying just pool + just yard + neither = 80 which is incorrect. I think it’s: just pool + just yard + both + neither = 80 and when you drop in the B’s you get 80=80 which doesn’t get you any new information.

Or using your variable names if it’s helpful:

(30-B)+39+B+11=80

This doesn’t help you solve for B.

But I might be wrong, I don’t usually solve these with equations but with a grid. If you do a grid for this one you end up with a row and a column with just one value in the spot you’re trying to solve which would point to not being enough info.

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