Question

19. 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. Find the number of months after which they will have the same number of CDs. Show your work.

Answer 1

Answer:  The answer is 3 months.

Step-by-step explanation:  Given that Tom has a collection of 30 CD's and Nita has a collection of 18 CD's. Tom is adding 1 CD a month to his collection while Nita is adding 5 CD's a month to her collection. We are to find the number of months after which both will have the same number of D's.

Let 'x' be the required number of months. Then, we will have

$30+1\times x=18+5\times x\\\\\Rightarrow 30+x=18+5x\\\\\Rightarrow 5x-x=30-18\\\\\Rightarrow 4x=12\\\\\Rightarrow x=3.$

Therefore, the number of months is 3.

Thus, the answer is 3 months.

Answer 2

M = number of months...
30 + m = 18 + 5m
30 - 18 = 5m - m
12 = 4m
12/4 = m
3 = m <== they will have the same amount at 3 months

check...
30 + 3 = 18 + 5(3)
33 = 18 + 15
33 = 33 (correct)