# Question Video: Evaluating Algebraic Expressions Involving Proportions

If 𝑥 : 𝑦 : 𝑧 = 3 : 4 : 8, then what is the value of (𝑥² + 𝑦² + 𝑧²)/(𝑦(𝑥 + 𝑧))?

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### Video Transcript

If the ratio of 𝑥 to 𝑦 to 𝑧 is three : four : eight, then what is the value of 𝑥 squared plus 𝑦 squared plus 𝑧 squared divided by 𝑦 multiplied by 𝑥 plus 𝑧.

We can see from the ratio given that our value of 𝑥 is equal to three, our value of 𝑦 is equal to four, and our value of 𝑧 is equal to eight. We can substitute these values directly into our expression. Three squared is equal to nine, four squared is 16, and eight squared is 64. So the numerator simplifies to nine plus 16 plus 64. We can simplify the denominator by using our order of operations known as PEMDAS or BIDMAS. We do the parentheses or brackets first, leaving us with four multiplied by 11. Nine plus 16 plus 64 is equal to 89. Four multiplied by 11 is 44.

The value of the expression 𝑥 squared plus 𝑦 squared plus 𝑧 squared divided by 𝑦 multiplied by 𝑥 plus 𝑧 is 89 over 44. This fraction can not be simplified as 89 and 44 have no common factor apart from one.