Question

Tina is saving to buy a notebook computer. She has two options. The first option is to put $300 awayinitially and save $30 every month. The second option is to put $100 away initially and save $50 everymonth. After how many months would Tina save the same amount using either option? How muchwould she save with either option?

Answer 1

The first step is to state the equations that describe the given situations.

The first one says that she can put $300 away and save $30 every month. This, written as an expression is:

`30x+300`

Where x is the number of months.

For the second option she can put $100 away and save $50 every month. This, written as an expression is:

`50x+100`

Now, to find how many months would Tina save the same amount of money using either options make both expressions equal and solve for x:

`\begin{gathered} 30x+300=50x+100 \\ 30x-50x=100-300 \\ -20x=-200 \\ x=(-200)/(-20) \\ x=10 \end{gathered}`

After 10 months she would have the same amount using either options.

To find how miuch would she save, use one of the expressions, any of them, and replace x for 10, for example, let's use the first expression:

`30(10)+300=600`

She will save $600 using either option.