Maths, word problems

Question

I would like to receive an explanation how to solve word questions like the one below, because they confuse me and I get lost when I'm trying to find something.

 

'Gary's motorbike uses petrol.

 

Gary needs to mix oil with the petrol.

He mixes oil with petrol in the ration 1:14 by volume.

 

Gary is going to ride his motorbike 3000 miles.

Each 20 miles he rides uses 1 litre of the oil and petrol mixture.

 

A 500ml bottle of oil costs 3.99.

 

Work out the total cost of the bottles of oil Gary needs to buy.

(1litre=1000ml)'

 

Thank you in advance

Answer 1

I understand how these can be confusing, and will share some ideas to help you. First, try & decide what it is that the question is asking - what answer are we looking for? Then look for other variables that play into that answer. I'm essentially asking you to look at the problem backward. Let me demonstrate.

 

The answer - "total cost of bottles of oil" - is dependent upon a couple of factors:

1. The number of bottles of oil needed for the trip;

2. The size & cost of each bottle.

 

As the size & cost of each bottle are given in the problem, we need to find how many bottles Gary needs. Look at the ratio of oil to petrol: the problem tells us that each liter of fuel is 1 part oil & 14 parts petrol (1:14). Realize that a 1:14 ratio indicates there are 15 parts of equal measure (1/15 oil + 14/15 petrol), and we will come back to this aspect after we know how much fuel Gary needs for the trip.

 

Now, Gary is said to drive 3000 miles, using 1 liter of fuel mixture every 20 miles. How many liters is that altogether? (3000 divided by 20). So Gary burns 150 liters of fuel during this trip.

 

Can we find out how much oil was used to make 150 liters of fuel? Of course! We already know that one-fifteenth of the fuel was oil - this was given to us in the problem. How quickly can we find 1/15 of 150? (150 liters times 1/15) or (150 liters divided by 15). I recommend that you write this out & show your work!

 

If Gary uses 10 liters of oil for this trip, how much did he pay for oil? We first have to find the number of bottles. Each bottle being 500 ml (half a liter), divide 10 liters by 1/2 (or divide 10000 ml by 500 ml). Again, write this out & show your work!

 

Finally, we can see that Gary bought 20 bottles of oil at $3.99 each. Write it out & show your work. Good luck!