Question

there were 69 players in a soccer league. the coach made 5 teams by putting x players on each team. then the coach made another team with 9 players on it. which tape diagram best represents the situation? three tape diagrams shown, first with five sections labeled x+9, total 69; second with five sections labeled x and one labeled 9, total 69; third with five sections labeled x and one labeled 69, total 9

Explanation:

Step1: Analyze the situation

There are 5 teams with \( x \) players each, so the total number of players in these 5 teams is \( 5x \). Then there is another team with 9 players. The total number of players in the soccer league is 69, so the equation representing this situation is \( 5x + 9=69 \).

Step2: Analyze each tape diagram

• First diagram: It shows 5 segments each labeled \( x + 9 \), which would represent \( 5(x + 9) \), not matching our situation.
• Second diagram: It shows 5 segments labeled \( x \) (representing the 5 teams with \( x \) players each) and 1 segment labeled 9 (representing the team with 9 players), with the total being 69. This matches the equation \( 5x+9 = 69 \).
• Third diagram: It has a total of 9 and a segment labeled 69, which does not match the situation.

Answer:

The second tape diagram (the one with five \( x \)-labeled segments and one 9 - labeled segment, with total 69)