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a contractor is purchasing some stone tiles for new patio each tile costs $3 and he wants to spend less than $1000 and it's less than $1,000 not less than or equal to a thousand the size of each tile is one square foot write an inequality that represents the number of tiles he can purchase with a one thousand dollar limit and then figure out how large the stone patio can be so let X let X be equal to the number of tiles purchased tiles purchased and so the cost of purchasing X tiles they're going to be three dollars each so it's going to be three X so three X is going to be the total cost of purchasing the tiles and he wants to spend less than $1000 three X is how much he spends if he buys X tiles it has to be less than $1000 we say it right there if it was less than or equal to it would have a little equal sign right there so if we want to solve for X how many tiles can he buy we can divide both sides of this inequality by three and because we're dividing or multiplying you can imagine we're multiplying by 1/3 or dividing by three because this is a positive number we do not have to swap the inequality sign so we are left with X is less than 1000 over 3 which is 333 and 1/3 so he has to buy less than 330 3 and 1/3 tiles that's how many tiles and each tile is one square foot so if you can buy less than 330 3 and 1/3 tiles then the patio has to be so the size of the patio size of the patio also has to be less than 333 and one third square feet feet squared we could say square feet and we're done