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Using a Tape Diagram to Solve Ratio Problems

Students surveyed boys and girls separately to determine which sport was enjoyed the most. After completing the boy survey, it was determined that for every 3 boys who enjoyed soccer, 5 boys enjoyed basketball. The girl survey had a ratio of the number of girls who enjoyed soccer to the number of girls who enjoyed basketball of 7:1. If the same number of boys and girls were surveyed, and 90 boys enjoy soccer how many girls enjoy each sport?


Boys

Step 1

that for every 3 boys who enjoyed soccer, 5 boys enjoyed basketball – That’s a ratio of 3:5. So, draw 3 boxes for soccer and 5 boxes for basketball.

Step 2

Since 90 boys enjoy soccer, divide 90 by 3 (the number of boxes drawn above for soccer) which is 30. So, each box represents 30 boys. Write 30 into each box.


Girls…

girls who enjoyed basketball of 7:1. …. Draw 7 boxes for soccer and 1 box for basketball

The ratio is 7:1. Remember, the same number of boys and girls were surveyed. And there are 8 girls in the ratio of 7:1. Notice, that 240 divided by 8 is 30.



Thus, 210 girls played soccer, and 30 girls played basketball. (The 210 comes from 30 x7, and 30 comes from (30 x 1).


 


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