Question

Tina is saving to buy a notebook computer. She has two options. The first option is to put $300 away

initially and save $10 every month. The second option is to put $100 away initially and save $30 every
month. After how many months would Tina save the same amount using either option? How much
would she save with either option?
After
months, Tina will save $
with either option.

Answer 1

Explanation:

The number of months is our unknown, which we will call x. y is the amount she saves. Representing the fact that she puts $10 away per month is 10x. If she puts $300 down initially and then adds 10 per month to that, the first equation is

y = 10x + 300

The same goes for the second option. Putting $30 away every month is represented as 30x, and if she is starting with 100 and adding 30 a month to it, the second equation is

y = 30x + 100

We are being asked to find the number of months where the amount Tina saves is equal. Since y is the amount Tina has saved and we want to know when these amounts are equal, we will set the equations equal to each other and solve for x, the number of months.

10x + 300 = 30x + 100 and

200 = 20x so

x = 10. After 10 months, Tina will have saved the same amount of money regardless of which option she has chosen. This is only true for 10 months though. After that, one will show more of a savings than the other.