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Algebra / Linear equations in two variables Difficulty: Medium

The equation $7 g + 7 b = 840$ $7 g + 7 b = 840$ represents the number of blue tiles, $b$ $b$ , and the number of green tiles, $g$ $g$ , an artist needs for an $840$ $840$ -square-inch tile project. The artist needs $71$ $71$ blue tiles for the project. How many green tiles does he need?

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Explanation

The correct answer is $49$ $49$ . It’s given that the equation $7 g + 7 b = 840$ $7 g + 7 b = 840$ represents the number of blue tiles, $b$ $b$ , and the number of green tiles, $g$ $g$ , an artist needs for an $840$ $840$ -square-inch tile project. It’s also given that the artist needs $71$ $71$ blue tiles for the project. Substituting $71$ $71$ for $b$ $b$ in the equation $7 g + 7 b = 840$ $7 g + 7 b = 840$ yields $7 g + 7 (71) = 840$ $7 g + 7 (71) = 840$ , or $7 g + 497 = 840$ $7 g + 497 = 840$ . Subtracting $497$ $497$ from both sides of this equation yields $7 g = 343$ $7 g equals 343$ . Dividing both sides of this equation by $7$ $7$ yields $g = 49$ $g equals 49$ . Therefore, the artist needs $49$ $49$ green tiles for the project.