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Studying for a test? Prepare with these 5 lessons on Solving inequalities.
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A contractor is purchasing some stone tiles for a new patio. Each tile costs $3, and he wants to spend less than $1,000. And it's less than $1,000, not less than or equal to $1,000. The size of each tile is one square foot. Write an inequality that represents the number of tiles he can purchase with a $1,000 limit. And then figure out how large the stone patio can be. So let x be equal to the number of tiles purchased. And so the cost of purchasing x tiles, they're going to be $3 each, so it's going to be 3x. So 3x is going to be the total cost of purchasing the tiles. And he wants to spend less than $1,000. 3x is how much he spends if he buys x tiles. It has to be less than $1,000, we say it right there. If it was less than or equal to, we'd 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 3. And because we're dividing or multiplying-- you could imagine we're multiplying by 1/3 or dividing by 3 -- because this is a positive number, we do not have to swap the inequality sign. So we are left with x is less than 1,000 over three, which is 333 and 1/3. So he has to buy less than 333 and 1/3 tiles, that's how many tiles, and each tile is one square foot. So if he can buy less than 333 and 1/3 tiles, then the patio also has to be less than 333 and 1/3 square feet. Feet squared, we could say square feet. And we're done.