I was wondering if anyone could provide me with a method to solving as I do not know what I am doing wrong after multiple attempts?

A portland cement sample contained 20% SiO2 by weight derived
from two silicate compounds, SiO2.2CaO and SiO2.3CaO that
are present in the cement in the mole ratio 3 : 4. Determine
the percent by weight of each silicate compound in the
cement.


Answer key from book : 24.57%, 43.43%


My answer: 36.03%, 63.09%


Assuming the first silicate compound as W1 & the second one as W2 and their overall composition contribution to the sample as 100%. I got one equation W1+W2= 357.4 and using the mole ratios given, I equated them to get W1= .564 \*W2. upon resubstituting that into the first equation, I got 128.8 g for W1 and 228.51 g for W2. Calculating the percentages for each, I got 36.03% and 63.9 % respectively. –


Note: I do find the percentages from the answer key weird too as they don't quite indicate a 100% composition contribution from the constituents. Or, maybe I am just missing something.


The help is much appreciated.




This problem seems to have wrong data ! Look !
The molar mass of $Ca\_2SiO\_4$ is $172$. The molar mass of $Ca\_3SiO\_5$ is $228$. If you mix $3$ moles $Ca\_2SiO\_4$, (= $516$ g), and $4$ moles $Ca\_3SiO\_5$, (= $912$ g), the total weight is : $516 + 912 = 1428$ g. This mixture contains $3+4 = 7$ moles of $SiO\_2$, which weighs $420$ g. In this mixture, the ratio $SiO\_2$/total mass = $420/1428$ = $29.4$%. Well. This is contrary to the initial data saying that the proportion of $SiO\_2$ is $20$% !!! Where is the mistake or the misconception ?


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