Question 1038089
s = weight of sugar
f = weight of flour
b = weight of butter.
t = weight of all 3 ingredients.


s = 3/5 * f
b = 5/6 * s = 5/6 * 3/5 * f = 15/30 * f = 1/2 * f


you have:


s = 3/5 * f
b = 1/2 * f


t = s + f + b = 3/5 * f + f + 1/2 * f = 6/10 * f + 10/10 * f + 5/10 * f = (6+10+5)/10 * f = 21/10 * f


you have:


s = 3/5 * f
b = 1/2 * f
t = 21/10 * f


from t = 21/10 * f, solve for f to get f = 10/21 * t


the ratio of sugar to flour is 3/5.
the ratio of flour to total is 10/21.


since 3/5 is equivalent to 6/10, you get:
the ratio of sugar to flour is 6/10
the ratio of flour to total is 10/21.


this means the ratio of sugar to flour to total is 6:10:21.


the total number of parts is 21.
6 of them are sugar.
10 of them are flour.
5 of them have to be butter.


since b = 1/2 * f, this makes sense.


since 100 grams more of flour was used than sugar, you get:
f = s + 100
this means that f - s = 100
since s = 3/5 * f, this means that f - 3/5 * f = 100
simplify to get 2/5 * f = 100
solve for f to get f = 5 * 100 / 2 = 250.


*****THIS IS WHERE I SCREWED IT UP PREVIOUSLY
*****THANKS FOR LETTING ME KNOW.


since f = s + 100, you get s = f - 100 = 150.


you wind up with:


f = 250
s = 150 


since b = 5/6 * s, then b = 750 / 6 = 125


you now have:
s = 150
f = 250
b = 125


since t = s + b + f, then t = 525.


150 grams of sugar and 250 grams of flour and 125 grams of butter were used to make the cake.


s = 3/5 * f becomes 150 = 3/5 * 250 which becomes 150 = 150.
this confirms the relationship between butter and flour is correct.


b = 5/6 * s becomes 125 = 5/6 * 150 which becomes 125 = 125.
this confirms the relationship between butter and sugar is correct.


we had a ratio of s:f:t = 6:10:21


the ratio of s:f:t in grams of each is 150:250:525


if you divide each of the grams by 25, you get a ratio of 6:10:21 which confirms the ratios are correct.