Question

Last month, Katie started training for the swim team. She swam 20 laps every day for 18 training days. This month, Katie wants to swim 215 more laps than last month. She will swim 3 more laps per training day and add more training days to her monthly schedule.

A. If Katie adds 5 training days to her schedule this month, will she swim 215 more laps?

B. If Katie adds 10 more training days to her schedule this month, will she swim 215 more laps?

C. If Katie adds 6 more training days to her schedule this month, will she swim 215 more laps?

D. Use the guess-check-generalize method to build an equation for finding the number of additional training days she needs to swim 215 more laps.

E. Solve your equation

Answer 1

Let x be the number of training days that Katie wants to add. In total she will have 18+x training days per month.

1. If Katie swam 20 laps every day for 18 training days, then she swam

`18\cdot 20=360` laps per month.

2. If Katie adds x training days and will swim 3 more laps per training day, then she will swim

`(18+x)\cdot (20+3)=23(18+x)=414+23x` laps per month.

3. If this month, Katie wants to swim 215 more laps than last month, then

`414+23x-360=215.`

Solve this equation:

`23x+54=215,\\ \\23x=215-54,\\ \\23x=161,\\ \\x=(161)/(23)=7.`

Therefore, it is sufficient to add 7 extra training days and 3 more laps each day to swim 215 laps more than last month. Moreover, if she adds more than 7 days (for example, 10 days), then she will swim more than 215 laps more.