Questions: Suppose C = 25y + 10 and y=30 x+15. Which of the following is equivalent to C=25 y+ 10, but written only in terms of x ? a.) C=75 x+45 b.) C=750 x+375 c.) C=750 x+385 d.) C=75 x+385

Suppose C = 25y + 10 and y=30 x+15. Which of the following is equivalent to C=25 y+ 10, but written only in terms of x ? a.) C=75 x+45 b.) C=750 x+375 c.) C=750 x+385 d.) C=75 x+385
Transcript text: 13:22 30 Question Tutorials 5 - Substitution in Multi-Step Linear Equations LEARNING OBJECTIVE: Use the Substitution Property of Equality to rewrite an expression for another variable. Suppose C = 25y + 10 and $y=30 x+15$. Which of the following is equivalent to $\mathrm{C}=25 \mathrm{y}+$ 10, but written only in terms of $x$ ? a.) $C=75 x+45$ b.) $C=750 x+375$ c.) $C=750 x+385$ d.) $C=75 x+385$ - app.sophia.org
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Solution

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Solution Steps

To solve this problem, we need to substitute the expression for \( y \) into the equation for \( C \). Given \( C = 25y + 10 \) and \( y = 30x + 15 \), we can replace \( y \) in the first equation with \( 30x + 15 \). Then, we simplify the resulting expression to find \( C \) in terms of \( x \).

Step 1: Substitute \( y \) in the equation for \( C \)

We start with the equations: \[ C = 25y + 10 \] and \[ y = 30x + 15. \] Substituting \( y \) into the equation for \( C \): \[ C = 25(30x + 15) + 10. \]

Step 2: Simplify the expression

Now, we simplify the expression: \[ C = 25 \cdot 30x + 25 \cdot 15 + 10. \] Calculating each term: \[ C = 750x + 375 + 10. \] Combining the constant terms: \[ C = 750x + 385. \]

Step 3: Identify the equivalent expression

We have derived that: \[ C = 750x + 385. \] Now, we compare this with the given options:

  • a.) \( C = 75x + 45 \)
  • b.) \( C = 750x + 375 \)
  • c.) \( C = 750x + 385 \)
  • d.) \( C = 75x + 385 \)

The correct equivalent expression is option c.

Final Answer

\(\boxed{C = 750x + 385}\)

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