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.

$392times 1.17 = €458.64$

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

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

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:

$3100 text{ metres} div 0.3048 text{ metres}= 10171text{ feet}$  (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$^3$:

$0.9times1.3times1.1=1.287$ 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:

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

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:

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

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$:

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

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