If one U.S. dollar equals 5.76 Egyptian pounds and one U.S. dollar equals 0.56 British pounds, how many Egyptian pounds equals one British pound?
A) 10.29 Egyptian pounds
B) 0.097 Egyptian pounds
C) 5.200 Egyptian pounds
D) 3.226 Egyptian pounds

Question

BlackTom AI · Accepted Answer

We start by organizing the given exchange rates: 1 US dollar (USD) equals 5.76 Egyptian pounds (EGP), and 1 USD equals 0.56 British pounds (GBP).

To compare EGP and GBP directly, convert GBP back to USD first. If 1 USD = 0.56 GBP, then 1 GBP = 1 / 0.56 USD.

Compute 1 / 0.56: since 0.56 = 56/100 = 14/25, its reciprocal is 25/14, which equals approximately 1.785714... USD per GBP.

Now convert that USD amount to EGP using the USD-to-EGP rate. Since 1 USD = 5.76 EGP, multiply: 1.785714... USD × 5.76 EGP/USD.

Do the exact calculation using fractions for precision: (25/14) USD × (576/100) EGP/USD = (25 × 576) / (14 × 100) EGP = 14400 / 1400 EGP = 72 / 7 EGP.

Compute 72/7 as a decimal: 72 ÷ 7 = 10.285714..., which rounds to approximately 10.29 EGP.

Now evaluate each answer choice:

- Option A: 10.29 Egyptian pounds. This matches the calculated value when rounding to two decimal places, so it is consistent with the conversion steps.

- Option B: 0.097 Egyptian pounds. This is far too small given the rates; it would imply a much larger USD value per GBP than the data supports, which contradicts the step-by-step conversion.

- Option C: 5.200 Egyptian pounds. This would be close to the direct USD-to-EGP rate if GBP were about 0.9 USD, which is not the case here; the actual GBP value in USD is about 1.785, leading to a much larger EGP amount.

- Option D: 3.226 Egyptian pounds. This is also inconsistent with the derived 72/7 EGP per GBP; it undervalues the amount relative to the precise calculation.

In summary, by chaining the given exchange rates (USD to GBP and USD to EGP) and performing the exact fractional calculation, the GBP-to-EGP amount is 72/7 ≈ 10.29 EGP, making Option A the correct choice observed from the comparison.

If one U.S. dollar equals 5.76 Egyptian pounds and one U.S. dollar equals 0.56 British pounds, how many Egyptian pounds equals one British pound? A) 10.29 Egyptian pounds B) 0.097 Egyptian pounds C) 5.200 Egyptian pounds D) 3.226 Egyptian pounds单项选择题

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