Tom has a collection of 30 CDs and Nita has a collection of 18 CDs Tom is adding one CD per month to his collection while Nita is adding five CDs per month to her collection after how many months will Tom and Nita have the same number of CDs right and solve a system of equations
Let's assume it takes 'x' months for Tom and Nita to have the same number of CDs.
After x months, Tom will have added x CDs to his collection, and Nita will have added 5x CDs to her collection.
Therefore, the total number of CDs Tom will have after 'x' months is 30 + x.
The total number of CDs Nita will have after 'x' months is 18 + 5x.
Since we want Tom and Nita to have the same number of CDs, we can set up the following equation:
30 + x = 18 + 5x
Subtracting x and 18 from both sides, we get:
30 - 18 = 5x - x
12 = 4x
Dividing both sides by 4, we get:
x = 3
Therefore, after 3 months, Tom and Nita will have the same number of CDs.
Solving a system of equations:
We can also solve the same problem by setting up a system of equations.
Let's assume it takes 'y' months for Tom and Nita to have the same number of CDs.
After y months, Tom will have added y CDs to his collection, and Nita will have added 5y CDs to her collection.
Therefore, the total number of CDs Tom will have after 'y' months is 30 + y.
The total number of CDs Nita will have after 'y' months is 18 + 5y.
Setting up a system of equations, we have:
30 + y = 18 + 5y --> y - 5y = 18 - 30 --> -4y = -12 --> y = 3
Therefore, after 3 months, Tom and Nita will have the same number of CDs, which confirms our previous answer.