Question

If the mean of a +1, a +4, a +7, a +8 and a + 10 is 12, find a

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Answer 1

Key Concepts

• Calculating the mean
• Solving algebraic equations

To find the mean of a set of numbers, we find their sum and divide it by the number of terms there are.

Solving the Question

We're given:

• The mean of (a + 1) + (a + 4) + (a + 7) + (a + 8) + (a + 10) is 12
• Find a

The sum of (a + 1) + (a + 4) + (a + 7) + (a + 8) + (a + 10) divided by 5 (because there are 5 numbers) is 12. Write this as an equation:

`12=((a + 1) + (a + 4) + (a + 7) + (a + 8) + (a + 10))/(5)`

Simplify:

`12=(a + 1 + a + 4 + a + 7 + a + 8 + a + 10)/(5)\\\\12=(5a + 30)/(5)\\\\12=a +6\\a=6`

Answer

a = 6