Question

the departure from the average is the difference between the actual amount of rain and the average amount of rain for a given month. the historical average for rainfall in albuquerque, nm for june, july, and august is shown in the table.

june	july	august

a. last june only 0.17 inches of rain fell all month. what is the difference between the average rainfall and the actual rainfall for last june?
inches

b. the departure from the average rainfall last july was -0.36 inches. how much rain fell last july? inches

c. how much rain would have to fall in august so that the total amount of rain equals the average rainfall for these three months?
inches

Explanation:

Part a

Step1: Identify values

Average for June: $0.67$, Actual for June: $0.17$

Step2: Calculate difference

Difference = Average - Actual = $0.67 - 0.17$
$0.67 - 0.17 = 0.5$

Step1: Recall departure formula

Departure = Actual - Average → Actual = Average + Departure

Step2: Substitute values

Average for July: $1.5$, Departure: $-0.36$
Actual = $1.5 + (-0.36) = 1.5 - 0.36$
$1.5 - 0.36 = 1.14$

Step1: Find total average rainfall

Total average = June avg + July avg + August avg = $0.67 + 1.5 + 1.57$
$0.67 + 1.5 = 2.17$; $2.17 + 1.57 = 3.74$

Step2: Let August actual be \( x \), set total actual = total average

June actual (from part a: $0.17$), July actual (from part b: $1.14$), August actual: \( x \)
So, $0.17 + 1.14 + x = 3.74$

Step3: Solve for \( x \)

$1.31 + x = 3.74$ → \( x = 3.74 - 1.31 \)
$3.74 - 1.31 = 2.43$

Answer:

$0.5$

Part b