Video: Solving Word Problems Involving the Mean

Before the last soccer game of the season, David scored a total of 23 goals. He scored 5 goals in the final game, with an average of 4 goals per game this season. To calculate the total number of games David played, we first find the sum of 23 and 5. What would be the next step? [A] add the sum to 4 [B] subtract four from 230 [C] multiply the sum by 4 [D] divide the sum by 4 [E] divide the sum by 5

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Video Transcript

Before the last soccer game of the season, David scored a total of 23 goals. He scored five goals in the final game with an average of four goals per game this season. To calculate the total number of games David played, we would first find the sum of 23 and 5. What would be the next step? Is it (A) add the sum to four, (B) subtract four from 230, (C) multiply the sum by four, (D) divide the sum by four, or (E) divide the sum by five?

In order to calculate the main average goals per game, we need to divide the total number of goals by the total number of games. In this question, we don’t know the total number of games, so we will let this be the letter 𝑛. We are told that the mean average is four. We are also told that David score 23 goals prior to the last game and five goals in the last game. This means that the total goals is the sum of 23 and five. Substituting these values into our formula gives us four is equal to 23 plus five divided by 𝑛.

23 plus five is equal to 28. So, we have four is equal to 28 divided by 𝑛. Multiplying both sides of this equation by 𝑛 gives us four 𝑛 is equal to 28. We can then divide both sides of this equation by four to calculate our value of 𝑛. 𝑛 is, therefore, equal to 28 divided by four. In order to calculate the total number of games that David played, the next step after finding the sum of 23 and five would be to divide this sum by four. This would give us a value for 𝑛 equal to seven. The total number of games that David played was seven.

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