Question

Tina is saving to buy a notebook computer. She has two options. The first option is to put $400 away initially and save $20 every month. The second option is to put $300 away initially and save $40 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

Her savings amounts after x months will be ...

... 400 + 20x

or

... 300 + 40x

You want to find x such that these are the same amount. So, we equate these values and solve for x.

... 400 + 20x = 300 + 40x

... 0 = -100 + 20x . . . . . . . . . subtract the left side

... 0 = -5 + x . . . . . . . . . . . . . divide by the coefficient of x

... 5 = x . . . . . . . . . . . . . . . . add the opposite of the constant

Using the first option, we find the savings amount to be

... 400 + 20·5 = 500

After 5 months, Tina will save $500 with either option.

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Once you have the expressions for the options, it is convenient to let a graphing calculator tell you the point where they are the same.