Ask a New Question
Menu

Question content area top

Part 1
Challenge  A foreign country uses the stellar as its currency. Before a trip to that​ country, Mia wants to exchange ​$1 comma 300 to stellars. Which of Bank A and Bank B has the better exchange​ rate? How many more stellars would she get if she exchanged her ​$1 comma 300 at the better exchange rate instead of at the other​ rate?
Bank A
Dollars​ ($)
Stellars
180
488
100
610
120
732
Bank B
0
25
50
0
60
120
180
240
300
Dollars ($)
Stellars

x y graph

Question content area bottom
Part 1
Which bank has the better exchange​ rate?
Bank Upper B
Bank Upper A
Your answer is correct.
Part 2
Mia would get
  
enter your response here more stellars if she exchanged her ​$1 comma 300 at the better exchange rate.
Which bank has the better exchange rate?Mia would getsheer@CNUM{1300}

1 answer

To determine which bank has a better exchange rate, we first need to assess the exchange rates provided by both banks.

Bank A Exchange Rates

  • $180 → 488 stellars
  • $100 → 610 stellars
  • $120 → 732 stellars

To calculate the exchange rates, we find out how many stellars you can get per dollar:

  1. For $180: \[ \text{Exchange Rate} = \frac{488 \text{ stellars}}{180 \text{ dollars}} \approx 2.71 \text{ stellars per dollar} \]

  2. For $100: \[ \text{Exchange Rate} = \frac{610 \text{ stellars}}{100 \text{ dollars}} = 6.10 \text{ stellars per dollar} \]

  3. For $120: \[ \text{Exchange Rate} = \frac{732 \text{ stellars}}{120 \text{ dollars}} \approx 6.10 \text{ stellars per dollar} \]

The best exchange rate at Bank A is 6.10 stellars per dollar.

Bank B Exchange Rates

From the data provided, let's estimate the rates for Bank B.

Let's assume the relevant exchange rate segments are near the dollar amounts where values are provided:

  1. For $0: 0 stellars
  2. For $25: (Assuming this linearly increases to around $50) (not given).
  3. For $50: 0 stellars
  4. For $60: 120 stellars
  5. For $120: Around $240

To find the exact exchange rate for Bank B at certain points, we'd require the respective stellar values at other exchanged dollar amounts.

However, it looks like we can see that the rate at $60 for Bank B is \( \frac{120}{60} = 2 \text{ stellars per dollar} \), and thus continues in a manner of changing, but given the current values, it'll still be less than what Bank A provides.

Conclusion

So, we establish from the figures:

  • Bank A has the better exchange rate of 6.10 stellars per dollar.
  • The best exchange rate you can get at Bank B (from the visible data) seems to be less than or around 2.71.

Part 2: Additional Stellars

Using Bank A:

  • For $1,300 at 6.10 stellars per dollar: \[ \text{Total Stellars} = 1300 \times 6.10 = 7930 \text{ stellars} \]

Using Bank B (assuming worst case 2 stellars per dollar): \[ \text{Total Stellars} = 1300 \times 2 = 2600 \text{ stellars} \]

Difference:

\[ 7930 - 2600 = 5330 \]

So, Mia would get 5,330 more stellars if she exchanged her $1,300 at Bank A instead of Bank B.

Thus the answer is:

  • Bank A has the better exchange rate.
  • She would get 5,330 more stellars.