Lilith is trying to break the world record for largest cap collection. She collects 3 caps per month in the first year, and 5 caps per month after the first year. Each Christmas, she also receives 40 caps from friends and family. She estimates that each year, she loses 15 of the caps she has collected. If Lilith has been collecting for 5 years, how many caps has she collected so far?
How many caps does Lilith collect in the first year? ** In the first year, Lilith collects 3 caps * 12 months = <<3*12=36>>36 caps.
How many caps does Lilith collect in each year after the first year? ** Every year afterwards, she collects 5 caps * 12 months = <<5*12=60>>60 caps.
How many years has Lilith collected caps? ** She does this for a total of 5 – 1 = <<5-1=4>>4 years.
How many caps has Lilith collected so far? ** This is a total of 60 caps * 4 years = <<60*4=240>>240 caps.
How many caps has Lilith collected so far? ** In total, she collects 36 + 240 = <<36+240=276>>276 caps by herself.
How many caps does Lilith receive over the Christmas? ** Over the Christmases, she receives 40 caps * 5 years = <<40*5=200>>200 caps from friends and family.
How many caps does Lilith lose over the years? ** She also loses 15 caps * 5 years = <<15*5=75>>75 caps over the years.
How many caps has Lilith collected so far? ** She has therefore collected 276 + 200 – 75 = <<276+200-75=401>>401 caps.
#### 401