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QuestionFind the cost of a Toronto car in USD using dimensional analysis. Choose the right fractions to cross-cancel units. Use 25000CAD25000 \mathrm{CAD} and 1USD/1.329CAD1 \mathrm{USD} / 1.329 \mathrm{CAD}. Round to the nearest dollar.

Studdy Solution

STEP 1

Assumptions1. The cost of the Toronto automobile is $25,000 CAD. The exchange rate is1 USD /1.329 CAD3. We want to find the cost of the automobile in USD4. The units of the fractions selected for dimensional analysis should cross-cancel to produce the unit of the desired answer (USD)

STEP 2

First, we need to set up our dimensional analysis equation. We want to convert the cost of the automobile from CAD to USD, so we need to multiply the cost in CAD by the exchange rate.
Cost in USD=Cost in CADtimesExchange rateCost\, in\, USD = Cost\, in\, CAD \\times Exchange\, rate

STEP 3

Now, plug in the given values for the cost in CAD and the exchange rate to calculate the cost in USD.
Cost in USD=$25,000 CADtimes1 USD1.329 CADCost\, in\, USD = \$25,000\, CAD \\times \frac{1\, USD}{1.329\, CAD}

STEP 4

Notice that the units of CAD in the numerator and denominator will cancel out, leaving us with the unit of USD.
Cost in USD=$25,000times11.329Cost\, in\, USD = \$25,000 \\times \frac{1}{1.329}

STEP 5

Calculate the cost in USD.
Cost in USD=$25,000times11.329=$18,812.64Cost\, in\, USD = \$25,000 \\times \frac{1}{1.329} = \$18,812.64

STEP 6

Round the cost to the nearest whole dollar.
Cost in USD=$18,813Cost\, in\, USD = \$18,813The cost of the Toronto automobile in U.S. Dollars is $18,813.

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