SOLUTION: 1. In a certain cookie recipe, the ratio of flour to cups of sugar is 3 to 1. If the recipe uses 2 1/4 cups of flour, how much sugar does it use?

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: 1. In a certain cookie recipe, the ratio of flour to cups of sugar is 3 to 1. If the recipe uses 2 1/4 cups of flour, how much sugar does it use?       Log On


   

Question 72867: 1. In a certain cookie recipe, the ratio of flour to cups of sugar is 3 to 1. If the recipe uses 2 1/4 cups of flour, how much sugar does it use?

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
If the ratio is 3 to 1, that means there is 3 times as much of the first object than the 2nd object. In this case, the amount of flour is triple the amount of sugar. In a simple case, say we have 6 cups of flour, we will have 2 cups of sugar (6/3=2). However, first you need to convert 2 1/4 to a simpler fraction by making it an improper fraction.
2+%281%2F4%29=9%2F4 Note: its not 2 multiplied by 1/4 its 2 and a fourth
Now we must set up a proportion
3%2F1=%289%2F4%29%2FxNotice that the amount of flour divided by the amount of sugar is 3.
%283%2F1%29%2A%284%2F9%29=%28cross%289%2F4%29%2Fx%29%2Across%284%2F9%29Multiply both sides by 4/9, this cancels the 9/4 on the right side
12%2F9=1%2FxMultiply the values on the left side
4%2F3=1%2FxSimplify the left side
4%2F3x=1Multiply both sides by x
cross%28%283%2F4%29%284%2F3%29%29x=3%2F4Multiply both sides by 3/4
x=3%2F4
Check:
%289%2F4%29%2F%283%2F4%29=3%2F1
%289%2Fcross%284%29%29%2A%28cross%284%29%2F3%29=3%2F1
9%2F3=3%2F1
3=3Works
So the amount of sugar is 3/4 of a cup. Hope this helps