During his shift at Pennant Sports Shop, Sam compared the items sold during last weekend's sale. There were 25 lacrosse sticks sold on Friday, 10 of which were defense sticks. There were 50 lacrosse sticks sold on Saturday, 15 of which were defense sticks. Did Pennant Sports Shop sell the same ratio of defense sticks to total lacrosse sticks on both days?

1 answer

To determine if Pennant Sports Shop sold the same ratio of defense sticks to total lacrosse sticks on both days, we can calculate the ratio for each day.

Friday:

  • Total lacrosse sticks sold: 25
  • Defense sticks sold: 10

The ratio of defense sticks to total lacrosse sticks on Friday is: \[ \text{Ratio on Friday} = \frac{\text{Defense sticks}}{\text{Total sticks}} = \frac{10}{25} = \frac{2}{5} \]

Saturday:

  • Total lacrosse sticks sold: 50
  • Defense sticks sold: 15

The ratio of defense sticks to total lacrosse sticks on Saturday is: \[ \text{Ratio on Saturday} = \frac{\text{Defense sticks}}{\text{Total sticks}} = \frac{15}{50} = \frac{3}{10} \]

Now, we need to compare the two ratios:

  • Ratio on Friday: \(\frac{2}{5}\)
  • Ratio on Saturday: \(\frac{3}{10}\)

To compare these fractions, we can convert them to a common denominator. The least common multiple of 5 and 10 is 10.

  • Convert \(\frac{2}{5}\): \[ \frac{2}{5} = \frac{2 \times 2}{5 \times 2} = \frac{4}{10} \]

Now we can compare:

  • Ratio on Friday (in terms of 10): \(\frac{4}{10}\)
  • Ratio on Saturday: \(\frac{3}{10}\)

Since \(\frac{4}{10} \neq \frac{3}{10}\), we find that the ratios are not the same.

Conclusion: Pennant Sports Shop did not sell the same ratio of defense sticks to total lacrosse sticks on both days.