08. Conversions

Question 1

LEVEL 4

An American car has a top speed of 120mp/h.

This car is exported to France so needs to have its speedometer change to km/h.

If 1 mile = 1.6 km, what will its top speed be in km/h?

Select the correct answer from the list below:

A: 120 km/h

B: 75 km/h

C: 192 km/h

D: 180 km/h

CORRECT ANSWER:   C: 192 km/h

WORKED SOLUTION:

Because the conversion is a simple 1 mile = 1.6 km, all we need to do to convert from miles to kilometres is multiply by 1.6.

120\times 1.6=192 km/h

Question 2

LEVEL 4

A person wishes to post a package that weighs 6.5 lb.

When they get to the post office, they’re told that the first 2 kg cost \pounds10 to post, and every other interval of 500 g over will cost an additional \pounds2.

If 1 lb = 453 g, how much will it cost to post the package?

Select the correct answer from the list below:

A: \pounds12

B: \pounds14

C: \pounds16

D: \pounds18

CORRECT ANSWER:   B: \pounds14

WORKED SOLUTION:

To start we need to convert the 6.5 lb to grams. Because 1 lb = 453g, all we need to do is multiply by 453.

6.5\times453=2944 g

Now that we have our weight in grams, we to split it up into two pieces: the first 2 kg and everything else. To do this, we need to remember that 2 kg = 2000 grams. This gives us:

2944-2000=944 g

So, our two pieces are 2 kg and 944 g. We are told that the 2 kg will cost £10, so need to find the cost of the 944 g, which we do by splitting it up into intervals of 500 g.

This gives us two intervals.

Because each interval costs £2, the additional cost will be:

This gives a total cost of:

Question 3

LEVEL 4

The current exchange rate between the British Pound and the Chinese Yuan is £1 = ¥8.80.

The cost of a large stuffed panda toy is ¥154.

The total cost for international shipping is ¥132 when you buy less than 10 pandas, every panda more costs ¥20 extra.

Given that the customs charge a 10\% import fee based on the value of a shipment’s contents, what is the total cost to buy 5 large stuffed pandas toys, in pounds?

Select the correct answer from the list below:

A: \pounds2768.48

B: \pounds112.75

C: \pounds111.25

D: \pounds125.25

CORRECT ANSWER:  C: \pounds111.25

WORKED SOLUTION:

To start, it is important to note that because the Chinese Yuan is bigger than the British Pound, we need to do some dividing to change from Yuan to Pound. Luckily, because we are told it is £1=¥8.80, we just need to divide by 8.80 to get £. Let’s start with the shipping fee.

Shipping Fee:

Because we are ordering less than 10, the shipping fee is ¥132.

Now, let’s look at the pandas.

Pandas:

But, this is just the cost for 1 panda and we want 5, so we need to multiply this by 5.

Now, we need to be careful when looking at the 10% import fee. We need to note that the fee only depends on the cost of the package’s contents (the pandas), and not delivery.

Import Fee:

And now, we just need to add everything together:

Question 4

LEVEL 4

Use the conversion chart below to find how many feet are in 2 yards.

Select the correct answer from the list below:

A: 3 feet

B: 1 foot

C: 9 feet

D: 6 feet

CORRECT ANSWER: D: 6 feet

WORKED SOLUTION:

To start, we need to find where 2 yards is by reading along the x-axis.

Then reading up to the line:

And now, all we need to do is read left to the y-axis.

So, there are 6 feet in 2 yards.

Question 5

LEVEL 4

Use the conversion graph below to find the number of kilometres in 3 miles.

Select the correct answer from the list below:

A: 4.7 km to 4.9 km

B: 3.6 km to 3.8 km

C: 1.7 km to 1.9 km

D: 2.8 km to 3 km

CORRECT ANSWER: A: 4.7 km to 4.9 km

WORKED SOLUTION:

Start by finding 3 miles on the y-axis.

Now read across to the line.

And finally, read down to the x-axis.

So there around 4.8 km in 3 miles, however any answer in between 4.7 km and 4.9 km is correct.

Question 6

LEVEL 4

Cristiano kicks a ball at 120 km/h. calculate the speed of the ball in m/s.

Select the correct answer from the list below:

A: 0.03 m/s

B: 33.3 m/s

C: 120000 m/s

D: 2000 m/s

CORRECT ANSWER: B: 33.3 m/s

WORKED SOLUTION:

First, convert the distance,

1 km = 1000 m

120 km = 120000 m

So, the speed of the ball is 120000 m per hour.

Then, convert the time,

1 minute = 60 seconds

1 hour = 60 minutes

1 hour = 60 \times 60 = 3600 seconds

Finally, divide the distance by the time to get the speed,

120000 \div 3600 = 33.3 m/s (1 dp)

Question 7

LEVEL 4

Achmed’s field measures 1700 m \times \, 900 m. What is the area of Achmed’s field in km^2?

Select the correct answer from the list below:

A: 1.53 km^2

B: 1.89 km^2

C: 1530 km^2

D: 1890 km^2

CORRECT ANSWER:       A: 1.53 km^2

WORKED SOLUTION:

The area of the field in m^2 is

1700 \times 900 = 1530000 m^2

We know that 1 km^2 = 1000 \times 1000 = 1000000 m^2.

So the area of the field in km^2 is

1530000 \div 1000000 = 1.53 km^2

Question 8

LEVEL 4

Ester buys a new pair of shoes. The shoe box measures 340 mm \times \, 250 mm \times \, 120 mm. What is the volume of the shoe box in cm^3?

Select the correct answer from the list below:

A: 10200000 cm^3

B: 102000 cm^3

C: 10200 cm^3

D: 102 cm^3

CORRECT ANSWER:       C: 10200 cm^3

WORKED SOLUTION:

The volume of the shoe box in mm^3 is

340 \times 250 \times 120 = 10200000 mm^3

We know that 1 cm^3 = 10 \times 10 \times 10 = 1000 mm^3.

So the volume of the shoe box in cm^3 is

10200000 \div 1000 = 10200 cm^3