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It takes 1 pound of flour to make y cakes. The price of flour is w dol
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21 Feb 2022, 06:19
21 Feb 2022, 06:19
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It takes 1 pound of flour to make y cakes. The price of flour is w dollars for x pounds. In terms of w, x and y, what is the dollar cost of the flour required to make 1 cake?
A. \(\frac{xy}{w}\)
B. \(\frac{y}{wx}\)
C. \(\frac{w}{xy}\)
D. \(\frac{wx}{y}\)
E. \(wxy\)
A. \(\frac{xy}{w}\)
B. \(\frac{y}{wx}\)
C. \(\frac{w}{xy}\)
D. \(\frac{wx}{y}\)
E. \(wxy\)
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Re: It takes 1 pound of flour to make y cakes. The price of flour is w dol
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21 Feb 2022, 06:27
21 Feb 2022, 06:27
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Carcass wrote:
It takes 1 pound of flour to make y cakes. The price of flour is w dollars for x pounds. In terms of w, x and y, what is the dollar cost of the flour required to make 1 cake?
A. \(\frac{xy}{w}\)
B. \(\frac{y}{wx}\)
C. \(\frac{w}{xy}\)
D. \(\frac{wx}{y}\)
E. \(wxy\)
A. \(\frac{xy}{w}\)
B. \(\frac{y}{wx}\)
C. \(\frac{w}{xy}\)
D. \(\frac{wx}{y}\)
E. \(wxy\)
These kinds of questions (Variables in the Answer Choices - VIACs) can be answered algebraically or using the INPUT-OUTPUT approach.
Let's use the INPUT-OUTPUT approach.
It takes 1 pound of flour to make y cakes.
Let's let y = 2, which means it takes 1 pound of flour to make 2 cakes.
So, 1 cake will require 0.5 pounds of flour
The price of flour is w dollars for x pounds.
Let's let w = 6 and x = 2, which means flour costs 6 dollars for 2 pounds.
In other words, flour costs 3 dollars per pound
Conclusion: If 1 cake will require 0.5 pounds of flour and flour costs 3 dollars per pound, then it will cost 1.5 dollars to make 1 cake.
In other words, when y = 2, w = 6 and x = 2, the answer to the question is 1.5 dollars
From here, we'll INPUT y = 2, w = 6 and x = 2 into each answer choice to see which one yields an OUTPUT of 1.5
A. \(\frac{(2)(2)}{6}\) = 4/6 = 0.66666.... We need an output of 1.5. ELIMINATE A
B. \(\frac{2}{(6)(2)}\) = 1/6 = 0.16666.... We need an output of 1.5. ELIMINATE B
C. \(\frac{(6)}{(2)(2)}\) = 6/4 = 1.5. GREAT!
D. \(\frac{(6)(2)}{2}\) = 6. We need an output of 1.5. ELIMINATE D
E. \((6)(2)(2)\) = 24. We need an output of 1.5. ELIMINATE E
Answer: C
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Re: It takes 1 pound of flour to make y cakes. The price of flour is w dol
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21 Feb 2022, 09:37
21 Feb 2022, 09:37
1
Think about this in terms of the units that are provided: we have 1 lb/y cakes or 1/y lb/cake. Furthermore, we have w $ / x lb or w/x $/lb.
All we have to do is look at the units to see how to multiply these together to make the units cancel out to get only cakes.
Starting from lb/cake and $/lb, we just need to get $/cake, which means simply multiply the two because the lb cancels right out. This of course leaves us with "dollars per (1) cake."
Therefore, we have 1/y lb/cake * w/x $/lb = (1/y)*(w/x) $/cake = w/xy $/cake. Answer C.
All we have to do is look at the units to see how to multiply these together to make the units cancel out to get only cakes.
Starting from lb/cake and $/lb, we just need to get $/cake, which means simply multiply the two because the lb cancels right out. This of course leaves us with "dollars per (1) cake."
Therefore, we have 1/y lb/cake * w/x $/lb = (1/y)*(w/x) $/cake = w/xy $/cake. Answer C.
