Farah predicts that the average text messages sent by her family will be 2042 messages each of the last 6 months in 2019. The number of text messages used during 5 of those months were 2800, 2481, 2105, 1975, 2732. How many text messages must be sent during the sixth month for her prediction to be true?

159 text messages

Step-by-step explanation:

Given that:

Predicted average = 2042

Number of months = 6

Number of texts for each of last 5 months :

Let number of text that must be sent in the sixth month = x

Predicted Average = (sum of texts / Number of months)

2042 = (2800 + 2481 + 2105 + 1975 + 2732 + x) / 6

2042 = (12093 + x) / 6

Cross multiply :

6 * 2042 = 12093 + x

12252 = 12093 + x

x = 12252 - 12093

x = 159