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Gcse aqa maths help please. Exam coming closer!

Please tell me how the answer to the question below is what it is.
Question= 3kg of apples and 1.5kg of blackberries cost £9.00
2kg and 4kg of blackberries cost £13.20.
Work out the cost of 1kg of apples and the cost of 1kg of blackberries.
You MUST show your working.



The answer is 1kg of apples = 1.80 and 1kg of blackberries is £2.40.
THE THING I DON'T UNDERSTAND IS THE STEPS TORWARDS WORKING OUT THE ANSWER :frown:
Here are those steps:

1)1 mark for 3a+1.5b = 9.00 or 2a+4b = 13.20
2) 1mark for 6a + 3b = 18 and 6a +12b = 39.6 M1
3) 1mark for 9b = 21.6
4) 2marks for answers Apples = 1.80 and Blackberries = 2.40
PLEASE WILL SOMEONE EXPLAIN STEP 2 AND 3 TO ME. I will be very grateful!
PS: (This is a 5 mark question on the higher tier paper).
Reply 1
Avatar for Jaymat
Jaymat
Its just asking you to put the information into two simultaneous equations, which allows you to mix the two equations into one in order to find the unknown values. 3kg of apples and 1.5kg berries turns into 3a+1.5b=9, while the 2nd equation is 2a+4b=13.2, as you can see on the steps.

Step 2 is just multiplying the equations to make the amounts of "a" equal, so you multiply 3a by 2 and 2a by 3. You need to multiply the whole equation by this which gives the two equations in step 2.

Because the values of "a" are equal, you can subtract the two equations to leave you with only the single unknown value "b" in the equation shown in step 3, allowing you to finish solving the equation for "b" as you can use 9b=21.6 to get it by dividing 21.6 by 9, which is 2.4. Then you can substitute 2.4 into either equation to find "a", if you used equation 2 then you would get 2a+9.60=13.20, rearranged into 2a=3.60, and finally a=1.80, leaving you with values for both a and b.
Ok thxs for replying...

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