"Jeremy is cooking using a recipe that requires flour, sugar and water. For each cup of sugar that Jeremy uses, he needs to use two cups of flour. He needs to use 2 1/2 more cups of water than flour. He also needs to use 3 1/2 cups less sugar than water. Find the amount of flour, sugar, and water that Jeremy needs."
I tried the problem and got these three equations:
2f = s
w = f + 2.5
w - 3.5 = s
The problem is (you've probably guessed it by now) that there is no set of matching variables to plug in. I have an exam tommorow and I am entirely lost. Please help.
Actually, I can't think of equations to model this problem, but what you've done shows that you understand the problem.
All I did from the first sentence was...
1c sugar
2c flour
That's directly from the first sentence. Then, it tells you that you need 2.5 more cups of water than flour, so just add that to the amount of flower. Check that with the sugar sentence, and it works out.
(It's strange that I can't think of equations for this problem. It would be interesting to see if someone else could.)
Thank you for your help. I'm still not entirely clear, but we'll probably go over the study guide before the exam, so I'll get a better understanding of it then. Once again, thank you for your help. :)
What is the relationship between shapes and other shapes
To solve this problem, let's use the equations you provided and try to find a solution.
The three equations you have are:
1. 2f = s (equation 1)
2. w = f + 2.5 (equation 2)
3. w - 3.5 = s (equation 3)
Let's begin by solving equation 2 for f:
w = f + 2.5
Subtracting 2.5 from both sides:
w - 2.5 = f (equation 4)
Now, substitute equation 4 into equation 1:
2f = s
2(w - 2.5) = s
2w - 5 = s (equation 5)
We now have two equations involving w and s, equation 3 and equation 5:
w - 3.5 = s (equation 3)
2w - 5 = s (equation 5)
To eliminate s, we can set the left-hand sides of both equations equal to each other:
w - 3.5 = 2w - 5
Now, solve for w:
w - 2w = -5 + 3.5
-w = -1.5
w = 1.5
Substitute the value of w into equation 3 to find s:
1.5 - 3.5 = s
-2 = s
Finally, substitute the values of s and w into equation 4 to find f:
f = w - 2.5
f = 1.5 - 2.5
f = -1
Uh oh! It seems that there is a problem with the given information. The negative values for f and s do not make sense in this context. It's possible that there has been an error either in the problem statement or in the provided equations.
To solve this problem accurately, it would be best to double-check the information and equations or consult with your teacher or classmates. Remember that it's important to have accurate and consistent information when solving mathematical problems.