Video: Writing and Solving Two-Step Linear Equations in a Geometric Context

Find the value of π‘Ž given the following information: 1) 𝑦 is on the line between π‘₯ and 𝑧. 2) π‘₯𝑦 = 24 cm. 3) 𝑦𝑧 = 8π‘Ž cm. 4) π‘₯𝑧 = 88 cm.

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Video Transcript

Find the value of π‘Ž given the following information: 𝑦 is on the line between π‘₯ and 𝑧. π‘₯𝑦 equals 24 centimeters, 𝑦𝑧 equals eight π‘Ž centimeters, and π‘₯𝑧 equals 88 centimeters.

We can begin this question by drawing the line π‘₯𝑧 on which 𝑦 lies. We’re told that π‘₯𝑦 equals 24 centimeters, 𝑦𝑧 equals eight π‘Ž centimeters, and the length of the whole line π‘₯𝑧 is 88 centimeters. The length from π‘₯𝑦 plus the length from 𝑦𝑧 is equal to the total distance from π‘₯ to 𝑧. As all of our measurements are in centimeters, this can be written as an equation. 24 plus eight π‘Ž is equal to 88. We can then solve this equation to calculate the value of π‘Ž. We begin by subtracting 24 from both sides. As 88 minus 24 is equal to 64, we have eight π‘Ž equals 64. We can then divide both sides of this new equation by eight. This gives us the value of π‘Ž equal to eight.

We can check this by substituting this value back in. From the line above, we actually know that eight π‘Ž is equal to 64. This means that the length of the line from 𝑦 to 𝑧 is 64 centimeters. As 24 centimeters plus 64 centimeters equals 88 centimeters, our answer is correct.

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