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 5 CDs 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 set up a system of equations to represent the number of CDs Tom and Nita have each month. Let's call the number of months x.
Tom's collection: 30 + x
Nita's collection: 18 + 5x
We want to find the value of x when their collections are equal, so we can set the two expressions equal to each other:
30 + x = 18 + 5x
Now we can solve for x:
Subtract 18 from both sides: 30 + x - 18 = 5x
12 + x = 5x
Subtract x from both sides: 12 = 4x
Divide both sides by 4: x = 3
After 3 months, Tom and Nita will have the same number of CDs.