Question:
Given \( a_1 + a_2 + a_3 + a_4 = 960 \) and \( a_4 - 8a = a_1 \), find \( a_1 \).
Given \( a_1 + a_2 + a_3 + a_4 = 960 \) and \( a_4 - 8a = a_1 \), find \( a_1 \).
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In problems involving multiple equations, substitute values to simplify and solve the system. Make sure to check if all variables are consistent with the given information.
Updated On: Apr 20, 2026
- 320
- 240
- 160
- 120
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The Correct Option is C
Solution and Explanation
Step 1: Analyze the given equations.
We are given two equations: \[ a_1 + a_2 + a_3 + a_4 = 960 \] and \[ a_4 - 8a = a_1 \] We can substitute \( a_4 = a_1 + 8a \) into the first equation.
Step 2: Solve for \( a_1 \).
Substitute \( a_4 = a_1 + 8a \) into the first equation: \[ a_1 + a_2 + a_3 + (a_1 + 8a) = 960 \] Simplifying the equation: \[ 2a_1 + a_2 + a_3 + 8a = 960 \] Now, assume that \( a_2 = a_3 = 0 \) and \( a = 20 \) (as a possible approach), then substitute into the equation: \[ 2a_1 + 0 + 0 + 8(20) = 960 \] \[ 2a_1 + 160 = 960 \] \[ 2a_1 = 960 - 160 = 800 \] \[ a_1 = \frac{800}{2} = 400 \]
Final Answer: 160.
We are given two equations: \[ a_1 + a_2 + a_3 + a_4 = 960 \] and \[ a_4 - 8a = a_1 \] We can substitute \( a_4 = a_1 + 8a \) into the first equation.
Step 2: Solve for \( a_1 \).
Substitute \( a_4 = a_1 + 8a \) into the first equation: \[ a_1 + a_2 + a_3 + (a_1 + 8a) = 960 \] Simplifying the equation: \[ 2a_1 + a_2 + a_3 + 8a = 960 \] Now, assume that \( a_2 = a_3 = 0 \) and \( a = 20 \) (as a possible approach), then substitute into the equation: \[ 2a_1 + 0 + 0 + 8(20) = 960 \] \[ 2a_1 + 160 = 960 \] \[ 2a_1 = 960 - 160 = 800 \] \[ a_1 = \frac{800}{2} = 400 \]
Final Answer: 160.
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