Grade 8 | Unit 4 | Lesson 1: Number Puzzles | Practice Problems

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Clare asks Andre to play the following number puzzle: Pick a number, Add 2, Multiply by 3, Subtract 7, Add your original number. Andre’s final result is 27. Which number did he start with?

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In a basketball game, Elena scores twice as many points as Tyler. Tyler scores four points fewer than Noah, and Noah scores three times as many points as Mai. If Mai scores 5 points, how many points did Elena score? Explain your reasoning.

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A store is designing the space for rows of nested shopping carts. Each row has a starting cart that is 4 feet long, followed by the nested carts (so 0 nested carts means there's just the starting cart). The store measured a row of 13 nested carts to be 23.5 feet long, and a row of 18 nested carts to be 31 feet long. How much does each nested cart add to the length of the row? Explain your reasoning.

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If the store design allows for 43 feet for each row, how many total carts fit in a row?

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Triangle A is an isosceles triangle with two angles of measure x degrees and one angle of measure y degrees. Find three combinations of x and y that make this sentence true.

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Write an equation relating x and y. If you were to sketch the graph of this linear equation, what would its slope be? How can you interpret the slope in the context of the triangle?

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Consider the following graphs of linear equations. Decide which line has a positive slope, and which has a negative slope. Then calculate each line’s exact slope.

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