The acidity of the water in a swimming pool is considered normal if the average of three pH readings is between 7.2 and 7.8, inclusive. The first two readings for a swimming pool are 7.4 and 7.9. What possible values for the third reading p will make the average pH normal?

the third reading should be between 6.3 and 8.1 for the acidity to be normal

Step-by-step explanation:

if the average m should be between 7.2 and 7.8, then

7.2 ≤ m ≤ 7.8

if m = (r₁+r₂+r₃) / 3, where r represents the readings, then:

(r₁+r₂+r₃) / 3 ≤ 7.8

but the fist reading r₁=7.4 and the second one r₂=7.9, then

(7.4+7.9+r₃) / 3 ≤ 7.8

7.4+7.9+r₃≤ 3*7.8

r₃≤ 3*7.8 - 7.4 - 7.9 = 8.1

then

r₃≤ 8.1

also 7.2 ≤ (r₁+r₂+r₃) / 3, then

7.2 ≤ (7.4+7.9+r₃) / 3

3 * 7.2 ≤ 7.4+7.9+r₃

3 * 7.2 - 7.4 - 7.9 ≤ r₃

6.3≤ r₃ → r₃ ≥6.3

if r₃ ≥6.3 and r₃≤ 8.1, then

6.3 ≤r₃≤ 8.1

the third reading should be between 6.3 and 8.1 for the acidity to be normal