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 Post subject: Year 8 Maths question PleasePosted: Sun Dec 08, 2019 9:52 pm

Joined: Sat Jan 03, 2015 5:26 pm
Posts: 269
Hi All

Question

Cameron mixes 100g of metal P and 200g of metal Q to make 300g of an alloy.

Metal P has a density of 17.5g/cm3. Metal Q has a density of 9.5g/cm3.

Calculate the density of the alloy to 3 significant figures

just in case

I calculated volume of P = 100/17.5
but confused on Volume of Q.

any help much appreciated

thanks

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 Post subject: Re: Year 8 Maths question PleasePosted: Sun Dec 08, 2019 10:23 pm

Joined: Wed May 09, 2007 3:09 pm
Posts: 1275
Location: Solihull, West Midlands
I think you're on the right lines - use the same method for the volume of Q

Now you know the volume of the alloy, and the total mass is 300g - then divide one by the other to get the overall density

(noting that the units of quantities like density helpfully tell you which way up to divide things!)

Also helps if you have a sense of whereabouts you expect the final answer to be - I'd be thinking "P is roughly twice as dense as Q, and I have half the mass of P to Q, so the volume of the alloy going to be mostly Q , and therefore the final density should be closer to Q's than to P's" (In my experience pupils will often write down any random number generated by their calculator without any "reality check" )

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 Post subject: Re: Year 8 Maths question PleasePosted: Sun Dec 08, 2019 10:23 pm

Joined: Sat Oct 13, 2018 5:00 pm
Posts: 340
The alloy is 1 part metal P : 2 parts metal Q.
So density of alloy is 1x (density of P) + 2 X (density of Q) all divided by 3.

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 Post subject: Re: Year 8 Maths question PleasePosted: Mon Dec 09, 2019 8:40 pm

Joined: Sat Jan 03, 2015 5:26 pm
Posts: 269
Thank you for trying both Solimum and Deb 70 but I needed the workings and answer but since you haven't provided that

please find what I have from my sons school teacher, and am confused as to why the Vol of Q = 300/9.5 rather than 200/9.5. I just need an explanation if someone can help .Many Thanks

Vol of P = 100/17.5 = 40/7

Vol of Q = 300/9.5=600/19

Density of alloy
D = M/V

400/40/7+600/19 which brings the answer to 5.53g/cm3

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 Post subject: Re: Year 8 Maths question PleasePosted: Tue Dec 10, 2019 12:51 pm

Joined: Wed Feb 28, 2007 12:30 pm
Posts: 463
Location: Harrow
1stly a quick sanity check will point out that 5.53g/cm3 can't be the correct answer as it is less then either of the metals.

I'd do it Dev70s way as that is the easiest.

so 3 cms3 would weigh (1 x 17.5g) + (2 x 9.5g )

=36.5g

1cm3 = 36.5g/3

12.2g (12.1666 to 2 sig figures)
therefore density is 12.2g cm3

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 Post subject: Re: Year 8 Maths question PleasePosted: Tue Dec 10, 2019 2:27 pm

Joined: Sat Sep 27, 2008 10:51 pm
Posts: 2561
Except that Deb70's way is wrong. The teacher's method (and solimum's) is correct, unfortunately the teacher has made a mistake and that's what is confusing OP.

1) You can't just take 1 x density A and 2 x density B and divide by 3 because you need to calculate the total volume so you can calculate the resulting density.

2) The teacher has made a mistake in saying 300/9.5, it should be 200/9.5, other than that this is the correct method.

Total volume is 100/17.5 + 200/9.5 = 5.714 + 21.053 = 26.767
Density = 300/26.767 = 11.208

The teacher's method supports the common sense "think about your answers" approach solimum suggests. 100/17.5 = 200/35 = "a bit less than 6"; 200/9.5 = 400/19 = "a bit more than 20".

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 Post subject: Re: Year 8 Maths question PleasePosted: Tue Dec 10, 2019 5:16 pm

Joined: Sat Jan 03, 2015 5:26 pm
Posts: 269
Thank you All for your suggestions and most of All.
Many Thanks Mike1880 for pointing out the errors.

Phew!!! now makes sense and I've emailed the teacher to point this OUT . ( surely must have been an oversight ) as answers have been posted on the school web site

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 Post subject: Re: Year 8 Maths question PleasePosted: Thu Dec 12, 2019 5:41 pm

Joined: Wed Feb 28, 2007 12:30 pm
Posts: 463
Location: Harrow
mike1880 you are correct, My fault for not reading the question properly as they are mixed by weight and not volume. Probably why I did so badly at my exams all those years ago.

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