SOLUTION: 23. In calcium sulfate the ratio, by mass, of calcium to sulfur is 5:4 and of calcium to oxygen is 5:8. How many grams of each are there in 34 g of calcium sulfate?

Question 1191857: 23. In calcium sulfate the ratio, by mass, of calcium to sulfur is 5:4 and
of calcium to oxygen is 5:8. How many grams of each are there in
34 g of calcium sulfate?
Found 2 solutions by math_tutor2020, greenestamps:
Answer by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!

The ratio of calcium to sulfur is 5:4
The ratio of calcium to oxygen is 5:8

We can flip the second ratio to get
ratio of oxygen to calcium is 8:5

Then join up the 8:5 ratio with the 5:4 ratio to get the triple ratio 8:5:4
This describes the ratio of oxygen to calcium to sulfur in that exact order.

Scale up that triple ratio by x to get 8x:5x:4x
The parts add to 8x+5x+4x = 13x+4x = 17x

Set this equal to the total amount of calcium sulfate () we have, which is 34 grams.
17x = 34
x = 34/17
x = 2

Therefore, the ratio 8x:5x:4x is 8*2:5*2:4*2 or 16:10:8

Telling us that there are...
16 grams of oxygen
10 grams of calcium
8 grams of sulfur
Each describes the mass value, and not weight.

Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

Calcium:sulfur = 5:4 = 5x:4x

Calcium:oxygen = 5:8 = 5x:8x

So calcium is 5x; sulfur is 4x, and oxygen is 8x; and the total is 34g.

5x+4x+8x=34
17x=34
x=2

ANSWERS:
calcium = 5x = 10g
sulfur = 4x = 8g
oxygen = 8x = 16g

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