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12 Jul 2023, 10:06
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
75% (01:43) correct
25%
(02:05)
wrong
based on 272
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Cake mix A is 80% flour and 20% sugar by weight. Cake mix B is 55% flour and 45% sugar by weight. If a mixture of mixes A and B is 65% flour by weight, what percent of the weight of the mixture consists of cake mix B?
A. 40%
B. 50%
C. 60%
D. 65%
E. 66.66%
A. 40%
B. 50%
C. 60%
D. 65%
E. 66.66%
12 Jul 2023, 10:51
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OE
The question asks what percent of the weight of the mixture consists of cake mix B. Map out the answer by setting up an expression that represents the weight of cake mix B in the mixture as a percent of the total weight of the mixture, .
The question provides information about the percentage of flour in cake mix A, cake mix B, and the mixture of A and B. Translate this information into an algebraic equation. Since cake mix A is 80% flour by weight, the weight of the flour in cake mix A can be expressed 0.8A. Since cake mix B is 55% flour by weight, the weight of the flour in cake mix B can be expressed 0.55B. Since the mixture of A and B is 65% flour by weight, the weight of the flour in the mixture can be expressed 0.65(A + B). Finally, the weight of the flour in the mixture of A and B is equal to the sum of the weight of flour in mix A and the weight of flour in mix B, so that 0.8A + 0.55B = 0.65(A + B). Distribute the 0.65 on the right side of the equation, so that 0.8A + 0.55B = 0.65A + 0.65B. Combine like terms, so that 0.15A = 0.1B. Multiply both sides of the equation by 10, so that 1.5A = B.
Now, substitute this value of B into the formula that represents the weight of cake mix B as a percent of the total weight of the mixture, so that . Simplify the expression, so that .
The correct answer is choice C.
The question asks what percent of the weight of the mixture consists of cake mix B. Map out the answer by setting up an expression that represents the weight of cake mix B in the mixture as a percent of the total weight of the mixture, .
The question provides information about the percentage of flour in cake mix A, cake mix B, and the mixture of A and B. Translate this information into an algebraic equation. Since cake mix A is 80% flour by weight, the weight of the flour in cake mix A can be expressed 0.8A. Since cake mix B is 55% flour by weight, the weight of the flour in cake mix B can be expressed 0.55B. Since the mixture of A and B is 65% flour by weight, the weight of the flour in the mixture can be expressed 0.65(A + B). Finally, the weight of the flour in the mixture of A and B is equal to the sum of the weight of flour in mix A and the weight of flour in mix B, so that 0.8A + 0.55B = 0.65(A + B). Distribute the 0.65 on the right side of the equation, so that 0.8A + 0.55B = 0.65A + 0.65B. Combine like terms, so that 0.15A = 0.1B. Multiply both sides of the equation by 10, so that 1.5A = B.
Now, substitute this value of B into the formula that represents the weight of cake mix B as a percent of the total weight of the mixture, so that . Simplify the expression, so that .
The correct answer is choice C.
13 Jul 2023, 02:13
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Given: Cake mix A is 80% flour and 20% sugar by weight. Cake mix B is 55% flour and 45% sugar by weight.
Asked: If a mixture of mixes A and B is 65% flour by weight, what percent of the weight of the mixture consists of cake mix B?
Let the percentage of the weight of the mixture consists of cake mix B be x.
65% = .65 = x 55% + (100%-x) 80% = .55x + .8 - .8x = .8 - .25x
.15 = .25x
x = 15/25 = 60%
IMO C
Asked: If a mixture of mixes A and B is 65% flour by weight, what percent of the weight of the mixture consists of cake mix B?
Let the percentage of the weight of the mixture consists of cake mix B be x.
65% = .65 = x 55% + (100%-x) 80% = .55x + .8 - .8x = .8 - .25x
.15 = .25x
x = 15/25 = 60%
IMO C
