1. The average (arithmetic mean) high temperature for x days is 70 degrees. The addition of one day with a high temperature of 75 degrees increases the average to 71 degrees. Quantity A Quantity Bx 5(A) Quantity A is greater.(B) Quantity B is greater.(C) The two quantities are equal.(D) The relationship cannot be determined from the information given.
Question
- The average (arithmetic mean) high temperature for x days is 70 degrees. The addition of one day with a high temperature of 75 degrees increases the average to 71 degrees. Quantity A Quantity Bx 5(A) Quantity A is greater.(B) Quantity B is greater.(C) The two quantities are equal.(D) The relationship cannot be determined from the information given.
Solution
Let's solve this step by step:
Step 1: Understand the problem The problem is asking us to compare the value of x (the original number of days) with the number 5.
Step 2: Set up the equations We know that the average temperature of x days is 70 degrees. So, the total temperature for these x days is 70x. When we add one more day of 75 degrees, the average becomes 71. So, the total temperature for these x+1 days is 71(x+1).
Step 3: Solve the equations We can set these two equations equal to each other and solve for x: 70x + 75 = 71x + 71 Subtract 70x from both sides: 75 = x + 71 Subtract 71 from both sides: x = 4
Step 4: Compare the quantities Now we can compare x (which is 4) with 5.
So, the answer is (B) Quantity B is greater.
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