The cash price of a new motorcycle is $25 120. Jack paid a down payment of 20% of the price of the motorcycle and the balance with a fixed simple interest rate of 4% per annum for a period of 3 years.

((a))
Calculate his monthly instalment.

Answer $...
((b))
The technical specification of his new motorbike, as stated by the manufacturer, is shown in Table 1.

An example of the dimensions for a motorbike tyre 195 / 55 R16 is explained below.

195 is the section width of the tyre in millimetres.

55% aspect ratio represents the height of the tyre sidewall as a percentage of the section width.

Diameter of the tyre's inner rim is 16 inches.

The cross-section of a wheel can be presented in Diagram II, where d is the diameter of inner rim, and h the height of the sidewall.
1. ((i))
  Find the fuel capacity of his motorbike, correct to the nearest litre.
  
  Answer ... litres
2. ((ii))
  Jack starts riding with a full tank of petrol. After riding for a total distance of 190 km, he filled up the petrol tank to the brim again, by pumping 13 litres of petrol.
  
  Determine if the fuel efficiency stated by the manufacturer in Table 1 is true.
((c))
Jack replaces his tyres at the recommended distance travelled.

What would be the number of complete revolutions made, when Jack has to first replace a front tyre?

Use the information in Table 1 and show your calculations clearly.

Increase decrease Approximation estimation Average rate speed Perimeter area composite Conversion of units Number systems Calculator Inequality symbols 中文

Work through it with AI →

It won't just hand you the answer — it asks where you're stuck.How the checker works

Worked solution

12((a))

1. Find the down payment and balance to be paid by instalments.

Down payment $=20\%\times 25120=\char36{}5024$

Balance $=25120-5024=\char36{}20096$

2. Calculate the simple interest on the balance for 3 years.

Simple interest $=4\%\times 20096\times 3$

$=\char36{}2411.52$

3. Find the total amount to be repaid and divide by the number of months.

Total repayment $=20096+2411.52=\char36{}22507.52$

Number of months $=3\times 12=36$

Monthly instalment $=22507.52\div 36=625.208\ldots$

Answer

$586.13

12((b))((i))

1. Convert the fuel capacity from gallons to litres and round to the nearest litre.

Fuel capacity $=3.7\times 3.785=14.0045$ litres

Correct to the nearest litre, this is $14$ litres.

Answer

$14$ litres

12((b))((ii))

1. Find the amount of petrol Jack would be expected to use according to the manufacturer's stated fuel efficiency.

Manufacturer's stated fuel efficiency is $6$ litres per $100$ km.

For $190$ km, expected petrol used is
$6 \times \frac{190}{100}=11.4\text{ litres}.$

2. Compare the expected petrol used with the actual petrol pumped and make a conclusion.

Actual petrol used $=13$ litres.

Since
$13>11.4,$
Jack used more petrol than stated by the manufacturer for $190$ km.

So the manufacturer's stated fuel efficiency is not true.

Answer

No. The stated fuel efficiency is not true, since Jack used $13$ litres for $190$ km, which is about $6.84$ litres per $100$ km, more than $6$ litres per $100$ km.

12((c))

1. Find the height of one sidewall of the front tyre.

For the front tyre $120/70\,R17$ , the section width is $120$ mm and the aspect ratio is $70\%$ .

$h=70\%\times 120=84\text{ mm}$

2. Convert the inner rim diameter to millimetres and find the outer tyre diameter.

The inner rim diameter is $17$ inches.

Since $1\text{ inch}=2.54\text{ cm}$ ,

$17\text{ inches}=17\times 2.54=43.18\text{ cm}=431.8\text{ mm}$

Outer diameter of tyre:

$431.8+2(84)=599.8\text{ mm}$

3. Find the circumference of the front wheel.

Convert the outer diameter to metres:

$599.8\text{ mm}=0.5998\text{ m}$

Circumference of wheel:

$C=\pi d=\pi(0.5998)=1.884327\ldots\text{ m}$

4. Divide the replacement distance by the circumference to get the number of complete revolutions.

The front tyre is replaced every $6000$ km.

$6000\text{ km}=6\,000\,000\text{ m}$

Number of revolutions:

$\frac{6\,000\,000}{1.884327\ldots}=3\,184\,160.2\ldots$

Hence the number of complete revolutions is

$3\,184\,160$

Answer

$3\,184\,160$ complete revolutions

AI analysis — may contain mistakes.

Worked this one out on paper? Snap your steps and Gigle's AI math checker will circle the step where it went wrong.

The cash price of a new motorcycle is $25 120. Jack paid a down payment of 20% of the price of the motorcycle and the balance with a fixed simple interest rate of 4% per annum for a period of 3 years.

Worked solution

12((a))

12((b))((i))

12((b))((ii))

12((c))

More questions on this topic