Tom has a collection of 30 cds and nita has a collection of 18 cds. tom is adding 1 cd a month to his collection while nita is adding 5 cds a month to her collection. write a system to find the number of months after which they will have the same number of cds. let x represent the number of months and y the number of cds. a. y = –x 30 y = 5x 18 2 months b. y = x 30 y = 18x 5 1 month c. y = x 18 y = 5x 30 33 months d. y = x 30 y = 5x 18 3 months

Tom has 30, and adding 1 CD a month.

After x months Tom would have had:   30 + x*1 =  30 + x,    y = 30 + x

Nita has 18, and adding 5 CDs a month.

After x months Nita would have had:   18 + x*5 =  18 + 5x,  y =  18 + 5x,

Solving the equation:

y = 30 + x,  y =  18 + 5x

30 + x = 18 + 5x

x - 5x = 18 - 30

-4x = -12

x = -12/-4

x = 3,      So after 3 months they would both have equal number.

System of equations:  y = 30 + x,   y =  18 + 5x,      will have same number after 3 months.