tom has a collection of 30 cds and nita has a collection of 18 cds. tom is adding 1 cd per month to his collection, while nita is adding 5cds per month to her collection. after how many months will tom and nita have the same number of cds? write and solve a system of equations
Let's call the number of months it takes for Tom and Nita to have the same number of CDs as "x".
After "x" months, Tom will have 30 + 1x CDs.
After "x" months, Nita will have 18 + 5x CDs.
Setting these two expressions equal to each other, we have the equation:
30 + 1x = 18 + 5x
Subtracting 18 from both sides, we get:
12 + 1x = 5x
Subtracting 1x from both sides, we get:
12 = 4x
Dividing both sides by 4, we get:
x = 3
Therefore, it will take Tom and Nita 3 months to have the same number of CDs.