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Question 1038089: The weight of sugar used to bake a cake was 3/5th the weight of flour used. The weight of butter used was 5/6th the weight of sugar used.
a. Find the ratio of the weight of sugar to the weight of flour to the total weight of the 3 ingredients.
b. If 100g more flour used than sugar, how much butter was used to bake the
cake?
Found 2 solutions by josmiceli, Theo:
Answer by josmiceli(19441)   (Show Source):
Answer by Theo(13342)  (Show Source):
You can put this solution on YOUR website! 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.
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