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Tyree currently has $12,500 in his bank account and Shanel has $14,000 in her bank account. Tyree deposits $275 per week and Shanel deposits $200 per week into her account. Write an equation to model this problem, where w represents the number of weeks they have been depositing. After how many weeks will they have the same amount of money?

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Answer:

They will have the same amount of money after 20 weeks.

Explanation:

After a careful reading to the statement of problem, we know that both Tyree and Shanel have saved money in two separate bank accounts and deposits weekly at same rate, which can be predicted by linear functions. That is:

Tyree

[tex]C_{T} = 12500 + 275\cdot w[/tex] (Eq. 1)

Shanel

[tex]C_{S} = 14000+200\cdot w[/tex] (Eq. 2)

Where:

[tex]C_{T}[/tex], [tex]C_{S}[/tex] - Money saved by Tyree and Shanel, measured in US dollars.

[tex]w[/tex] - Number of weeks, dimensionless.

If we assume that [tex]C_{T} =C_{S}[/tex], then we solve the resulting equation for [tex]w[/tex]:

[tex]12500+275\cdot w = 14000+200\cdot w[/tex]

[tex]75\cdot w = 1500[/tex]

[tex]w = 20[/tex]

They will have the same amount of money after 20 weeks.

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