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

Find the value of π‘Ž given the following information: π‘Œ is on the line between 𝑋 and 𝑍. π‘‹π‘Œ = 24 cm. π‘Œπ‘ = 8π‘Ž cm. 𝑋𝑍 = 88 cm.

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Video Transcript

Find the value of π‘Ž given the following information: π‘Œ is on the line between 𝑋 and 𝑍. π‘‹π‘Œ equals 24 centimeters, π‘Œπ‘ equals eight π‘Ž centimeters, and 𝑋𝑍 equals 88 centimeters.

We can begin this question by drawing the line 𝑋𝑍 on which π‘Œ lies. We’re told that π‘‹π‘Œ equals 24 centimeters, π‘Œπ‘ equals eight π‘Ž centimeters, and the length of the whole line 𝑋𝑍 is 88 centimeters. The length from π‘‹π‘Œ plus the length from π‘Œπ‘ is equal to the total distance from 𝑋 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 π‘Œ to 𝑍 is 64 centimeters. As 24 centimeters plus 64 centimeters equals 88 centimeters, our answer is correct.

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