evelync12
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A sample of strontium has a relative atomic mass of 87.7 and consists of three
8687 88
isotopes, Sr, Sr and Sr 86 87
In this sample, the ratio of abundances of the isotopes Sr : Sr is 1:1
State why the isotopes of strontium have identical chemical properties. Calculate the percentage abundance of the 88Sr isotope in this sample.


I've managed to get this: 86x + 87x + 88(100-2x)/100 = 87.7
but because i'm bad at algebra, i have no idea how to go from there. please can someone lay out their working from this point to get the answer?
the answer is: 80%
i know it's a lot to ask but i'm really struggling to get round this algebra
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Abigail0091
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That information can be used to create two simultaneous equations that can then be solved.
The first is 86x+87x+88y=87.7 which simplifies to 173x+88y=87.7
The second is 2x+y=1
As the ratio is 1:1 for 86 and 87 which is 2x and then 88 is another unknown e.g. y and the total must be 1
Multiply equation 2 by 88 to get 176x+88y=88 (3)
Subtract this equation (3) from equation 1 to get -3x=-0.3 and then flip this to get 3x=0.3 so x=0.1
Put this back into the original equation (2) to get 2(0.1)+y=1 so 0.2+y=1 and y=0.8 and therefore 80%

Your equation can also be used when simplified in a similar way:
Simplify: 173x+88(100-2x)=8770
173x+8800-176x=8770
-3x+8800-176x=8770
-3x=-30
x=10
Then use 2x+y=100
2(10)+y=100
y=80
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Abigail0091
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(Original post by Abigail0091)
That information can be used to create two simultaneous equations that can then be solved.
The first is 86x+87x+88y=87.7 which simplifies to 173x+88y=87.7
The second is 2x+y=1
As the ratio is 1:1 for 86 and 87 which is 2x and then 88 is another unknown e.g. y and the total must be 1
Multiply equation 2 by 88 to get 176x+88y=88 (3)
Subtract this equation (3) from equation 1 to get -3x=-0.3 and then flip this to get 3x=0.3 so x=0.1
Put this back into the original equation (2) to get 2(0.1)+y=1 so 0.2+y=1 and y=0.8 and therefore 80%

Your equation can also be used when simplified in a similar way:
Simplify: 173x+88(100-2x)=8770
173x+8800-176x=8770
-3x+8800-176x=8770
-3x=-30
x=10
Then use 2x+y=100
2(10)+y=100
y=80
The key thing here is to expand the brackets and to multiply out the /100 so that you can have all the x's on one side and the normal numbers on the otherside
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evelync12
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(Original post by Abigail0091)
That information can be used to create two simultaneous equations that can then be solved.
The first is 86x+87x+88y=87.7 which simplifies to 173x+88y=87.7
The second is 2x+y=1
As the ratio is 1:1 for 86 and 87 which is 2x and then 88 is another unknown e.g. y and the total must be 1
Multiply equation 2 by 88 to get 176x+88y=88 (3)
Subtract this equation (3) from equation 1 to get -3x=-0.3 and then flip this to get 3x=0.3 so x=0.1
Put this back into the original equation (2) to get 2(0.1)+y=1 so 0.2+y=1 and y=0.8 and therefore 80%

Your equation can also be used when simplified in a similar way:
Simplify: 173x+88(100-2x)=8770
173x+8800-176x=8770
-3x+8800-176x=8770
-3x=-30
x=10
Then use 2x+y=100
2(10)+y=100
y=80
thank you so much
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