Question

Tiffany is borrowing $1200 from her parents to buy a new laptop computer. She plans to pay them back at the rate of $70 a month. Rosie is borrowing $900 from her parents to buy a violin. She plans to pay her parents back at the rate of $40 per month.

PART A

Write an equation that can be used to determine after how many months the girls will owe the same amount.

PART B:

Determine algebraically and state in how many months the two girls will owe the same amount. State the amount they will owe at this time.

PART C

Tiffany claims that she will have her loan paid off 8 months after she and Rosie owe the same amountDetermine and state if Tiffany is correct. Explain your reasoning.

Answer 1

Step-by-step explanation:

PART A:

To determine after how many months the girls will owe the same amount, we can set up an equation based on the amounts borrowed and the repayment rates.

Let's denote the number of months as "m".

For Tiffany, the amount owed after "m" months can be calculated as: 1200 - 70m.

For Rosie, the amount owed after "m" months can be calculated as: 900 - 40m.

PART B:

To find the number of months when the two girls will owe the same amount, we set their respective equations equal to each other:

1200 - 70m = 900 - 40m

Let's solve this equation algebraically:

1200 - 900 = 70m - 40m

300 = 30m

Dividing both sides by 30:

10 = m

Therefore, after 10 months, both girls will owe the same amount.

To find the amount they will owe at this time, substitute the value of "m" into either equation. Let's use Tiffany's equation:

Amount owed by Tiffany after 10 months:

1200 - 70(10) = 1200 - 700 = $500

Therefore, after 10 months, both girls will owe $500.

PART C:

Tiffany claims that she will have her loan paid off 8 months after she and Rosie owe the same amount. To verify if Tiffany is correct, we need to find the amount she will owe 8 months after owing the same as Rosie.

Using Tiffany's equation, let's substitute "m" with 10 (since that's when they owe the same amount):

Amount owed by Tiffany after 10 months:

1200 - 70(10) = 500

Now, let's determine the amount Tiffany will owe after 8 more months:

Amount owed by Tiffany after 10 months + 8 more months:

500 - 70(8) = 500 - 560 = -60

Tiffany will owe -$60 after 8 more months. However, a negative amount does not make sense in this context. So, Tiffany's claim is incorrect. She will not have her loan paid off 8 months after they owe the same amount.

Therefore, Tiffany's claim is not correct.