Question:
Ten friends wish to raise funds for a get-together. Six of them contributed \(\$ 60\) each while each of the other four friends contributed \(\$ 60\) more than the average contribution of all ten friends. What was the total contribution of the ten friends?
Ten friends wish to raise funds for a get-together. Six of them contributed \(\$ 60\) each while each of the other four friends contributed \(\$ 60\) more than the average contribution of all ten friends. What was the total contribution of the ten friends?
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When dealing with total contributions where some individuals contribute more than others, set up an equation based on the average to find the total.
Updated On: Sep 30, 2025
- $ 100
- $ 600
- $ 800
- $ 1000
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The Correct Option is D
Solution and Explanation
Step 1: Define variables.
Let the average contribution be \( x \). The total contribution from the six friends is \( 6 \times 60 = 360 \). Each of the other four friends contributed \( x + 60 \), so their total contribution is \( 4 \times (x + 60) \).
Step 2: Set up the equation.
The total contribution of all ten friends is the sum of the contributions of the six friends and the four friends: \[ 6 \times 60 + 4 \times (x + 60) = 10 \times x. \] Simplifying: \[ 360 + 4x + 240 = 10x, \] \[ 600 = 6x, \] \[ x = 100. \]
Step 3: Calculate the total contribution.
The total contribution is \( 10 \times x = 10 \times 100 = 1000 \).
Final Answer: \[ \boxed{1000} \]
Let the average contribution be \( x \). The total contribution from the six friends is \( 6 \times 60 = 360 \). Each of the other four friends contributed \( x + 60 \), so their total contribution is \( 4 \times (x + 60) \).
Step 2: Set up the equation.
The total contribution of all ten friends is the sum of the contributions of the six friends and the four friends: \[ 6 \times 60 + 4 \times (x + 60) = 10 \times x. \] Simplifying: \[ 360 + 4x + 240 = 10x, \] \[ 600 = 6x, \] \[ x = 100. \]
Step 3: Calculate the total contribution.
The total contribution is \( 10 \times x = 10 \times 100 = 1000 \).
Final Answer: \[ \boxed{1000} \]
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