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. if katie adds 5 training days to her schedule this month, will she swim 215 more laps? if katie adds 10 more training days to her schedule this month, will she swim 215 more laps? if katie adds 6 more training days to her schedule this month, will she swim 215 more laps? build an equation for finding the number of additional training days she needs to swim 215 more laps.

She swim 20 laps every day for 18 training days

so total laps done last month = 20*18 = 360 laps

She will swim 3 more laps per training day and add more training days to her monthly schedule.

20 laps + 3 laps = 23 laps

(a)If Katie adds 5 training days to her schedule this month, will she swim 215 more laps?

18 days + 5 days more = 23 days

23 laps every day for 23 training days

so total laps = 23*23 = 529 laps. That is 169 more laps than 360 laps done last month. Hence she cannot swim 215 more laps

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

18 days + 10 days more = 28 days

23 laps every day for 28 training days

so total laps = 23*28 =644 laps. That is 284 more laps than 360 laps done last month. Hence she can swim 215 more laps

(c)If Katie adds 6 more training days to her schedule this month, will she swim 215 more laps?

18 days + 6 days more = 24 days

23 laps every day for 24 training days

so total laps = 23*24 =552 laps. That is 192 more laps than 360 laps done last month. Hence she cannot swim 215 more laps

Build an equation for finding the number of additional training days she needs to swim 215 more laps

Let x be the number of days more

So training days = 18 + x

215 more laps , so total laps = 360 + 215 = 575

3 more laps per training day so 20 + 3 = 23 laps per day

laps * training days = total laps

so equation becomes

23 * (18+x) = 575

Now solve for x

414 + 23x = 575

Subtract 414 from both sides

23x = 161

x= 7

so she needs 7 training days to swim 215 more laps

x= -3 and

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

where a is the cube root of .

here   this is 27 and the cube root of 27 is 3. so we write using the form:

.

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

where a = 1, b=3, and c=9

this cubic has two complex roots.