Functional Skills: Unit Conversions

We can either deduct the 2\% commission from the amount in pounds at the start or from the amount in euros at the end.

A 2\% decrease means she will have 98\% of her money left over, so

 

\text{Money left } = \dfrac{98}{100} \times 400 = \pounds 392

 

Using the conversion rate given in the question, we can find out how much £392 is in euros.

 

392\times 1.17 = €458.64

The conversion rate is between metres and feet, so first we need to convert 3.1km into metres. We know that 1km is 1000m, so:

 

3.1\text{km} = 3.1 \times 1000 \text{m} = 3100\text{m}

 

If 1 foot is equal to 0.3048 metres, that means we would have to multiply a distance in feet by 0.3048 in order to get the equivalent distance in metres. So, to go from metres to feet, we will have to divide by 0.3048. This means Meghan’s walk in feet is:

 

3100 \text{ metres} \div 0.3048 \text{ metres}= 10171\text{ feet}  (to nearest foot)}

Converting the measurements from cm to m first:

90 cm = 0.9 m

130 cm = 1.3 m

110 cm = 1.1 m

 

Then calculate the volume of the container in m^3:

0.9\times1.3\times1.1=1.287 m^3

 

Finally, convert to litres:

1.287 m^3 = 1287 L

We first need to convert the distance of the race from miles to kilometres, as the average pace has been given in minutes per kilometre. We can convert 10 miles into kilometres as follows:

 

10 \text{ miles} \times 1.61 \text{ kilometres} = 16.1\text{ kilometres}

 

If it takes the runner 6 minutes and 12 seconds to run one kilometre, then we simply need to multiply 16.1 kilometres by the runner’s pace.

 

 

6 \text{ minutes } 12 \text{ seconds} \equiv 6.2 \text{ minutes}

(Remember that 12 seconds is \frac{1}{5} a minute = 0.2 minutes)

 

The total time to complete the 10 mile race at a pace of 6.2 minutes per kilometre is therefore:

 

16.1\text{ kilometres} \times 6.2\text{ minutes per kilometre} = 99.82\text{ minutes}

 

The question says that we can round the answer to the nearest minute, so the half marathon will take 100 minutes, which is 1 hour and 40 minutes.

 

If the businessman exchanges £3500 into dollars in January, we need to calculate how many dollars he receives. If £1 equates to \$1.40, then £3500 can be converted as follows:

 

\pounds 3500 \times \$1.40= \$4900

 

If he trades the \$4900 back into pounds in February, we need to calculate how many pounds he will receive. The exchange rate is \$1.37 to the pound, so we need to see how many times \$1.37 goes into \$4900:

 

\$4900\div \$1.37= \pounds 3577 (to the nearest pound).

 

If the businessman started with £3500 and ended up with £3577, he has made a profit of £77.