Sharon has collected donations of $4.40, $3.12, $8.00, and $6.22 to help buy books for the new library. What is the mean (average) amount of donations she has collected?

5.435

Step-by-step explanation: In math, the average value in a set of numbers is the middle value, calculated by dividing the total of all the values by the number of values. To find this answer, we need to find the average of a set of data, we add up all the values and divide this total by the numbers of values. So if you add 4.40, 3.12, 8.00 and 6.22 together, we get 21.74. There are four values (4.40, 3.12, 8.00 and 6.22) so we divide the amount of values there are, which would be four. 21.47/4 would then get you 5.435

Since we want to solve for the variable x, we want to isolate x

a²x + (a - 1) = (a + 1)x ⇒ Distribute x to (a+1). Also, remove parentheses

a²x + a - 1 = ax + x ⇒ Subtract a from both sides

a²x - 1 = ax + x - a ⇒ Add 1 to both sides

a²x = ax + x - a + 1 ⇒ Subtract (ax + x) from both sides

a²x - (ax + x)= ax + x - a + 1 - (ax+x) ⇒ Simplify. Remember that multiplying positive by negative = negative

a²x - ax - x = ax + x - a + 1 - ax - x ⇒ Simplify

a²x - ax - x = -a + 1 ⇒ Factor out the x from a²x - ax - x

x(a² - a - 1) = -a + 1 ⇒ Divide both sides by (a² - a - 1)

x = (-a + 1) / (a² - a - 1)

However, we need to make sure that the denominator does not equal 0. Therefore, you set the denominator = 0 (just use the quadratic formula for this), and it gives that the denominator =0 when a = (1+√5)/2 AND (1-√5)/2

Therefore, the final answer is

x = (-a + 1) / (a² - a - 1) given that a ≠ (1+√5)/2, a ≠ (1-√5)/2