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JulijaS [17]
3 years ago
11

Tina is saving to buy a notebook computer. She has two options. The first option is to put $500 away initially and save $10 ever

y 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?
Mathematics
1 answer:
Alexxandr [17]3 years ago
3 0

Answer:

Tina would save the same amount using either option after 20 months.

With either option, Tina would save $700.

Step-by-step explanation:

This problem can be modeled by a first order equation:

Where Tina's saved money after n months is:

S(n) = S(0) + rn, where S(0) is the money put away initially and r is how much she saves every month.

The first option is to put $500 away initially and save $10 every month, so:

S_{1}(n) = 500 + 10n

The second option is to put $100 away initially and save $30 every month, so:

S_{2}(n) = 100 + 30n

After how many months would Tina save the same amount using either option?

It will happen at the month n in which S_{1}(n) = S_{2}(n), so:

S_{1}(n) = S_{2}(n)

500 + 10n = 100 + 30n

500 - 100 = 30 - 10n

400 = 20n

20n = 400

n = \frac{400}{20}

n = 20.

Tina would save the same amount using either option after 20 months.

How much would she save with either option?

We can choose S_{1}(20) or S_{2}(20), since they are equal

S_{1}(20) = 500 + 10(20) = 500 + 200 = 700

With either option, Tina would save $700.

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