Papayaya, a popular soft drink, contains only four ingredients. Soda water comprise 4/7 of Papayaya and natural lemon juice makes 1/3 of Papayaya. The amounts of sugar and papaya puree in Papayaya are equal. Due to a malfunction, the mixing machine mixes double the regular amount of lemon juice and three times the regular amount of papaya puree. If no other changes were made to the relative quantities of the ingredients, what is the fractional portion of soda water in the drink that comes out of the malfunctioning machine?
A. 7/30
B. 7/21
C. 2/5
D. 12/29
E. 4/7
Can some experts show how will i solve this problem?
OA C
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Papayaya
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You said: "Due to a malfunction, the mixing machine..."
But I hardly think a mixing machine can be due to a malfunction.
But I hardly think a mixing machine can be due to a malfunction.
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Recipe:lheiannie07 wrote:Papayaya, a popular soft drink, contains only four ingredients. Soda water comprise 4/7 of Papayaya and natural lemon juice makes 1/3 of Papayaya. The amounts of sugar and papaya puree in Papayaya are equal. Due to a malfunction, the mixing machine mixes double the regular amount of lemon juice and three times the regular amount of papaya puree. If no other changes were made to the relative quantities of the ingredients, what is the fractional portion of soda water in the drink that comes out of the malfunctioning machine?
A. 7/30
B. 7/21
C. 2/5
D. 12/29
E. 4/7
Soda = 4/7.
Lemon = 1/3.
Remainder = 1/2 sugar, 1/2 puree.
Let the total recipe = the LCM of 7, 3 and 2 = 42.
Original values:
Soda = (4/7)(42) = 24.
Lemon = (1/3)(42) = 14.
Remainder = 42-24-14 = 4, implying that sugar = 2 and that puree = 2.
After the malfunction:
Lemon doubled = 2*14 = 28.
Puree tripled = 3*2 = 6.
Soda unchanged = 24.
Sugar unchanged = 2.
New total = 28+6+24+2 = 60.
Resulting fraction:
soda/(new total) = 24/60 = 2/5.
The correct answer is C.
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We see that the correct amount of papaya puree as a fraction of the Papayaya drink is: (1 - 4/7 - 1/3)/2 = (21/21 - 12/21 - 7/21)/2 = (2/21)/2 = 1/21. Thus, the amount of sugar is also 1/21.lheiannie07 wrote:Papayaya, a popular soft drink, contains only four ingredients. Soda water comprise 4/7 of Papayaya and natural lemon juice makes 1/3 of Papayaya. The amounts of sugar and papaya puree in Papayaya are equal. Due to a malfunction, the mixing machine mixes double the regular amount of lemon juice and three times the regular amount of papaya puree. If no other changes were made to the relative quantities of the ingredients, what is the fractional portion of soda water in the drink that comes out of the malfunctioning machine?
A. 7/30
B. 7/21
C. 2/5
D. 12/29
E. 4/7
Thus, the ratio of soda water to lemon juice to sugar to papaya puree is 12:7:1:1.Now let's double the amount of lemon juice and triple the amount of papaya puree, which changes the ratio to 12:14:1:3. We see that soda water is now
12/(12 + 14 + 1 + 3) = 12/30 = 2/5 of the drink from the malfunction machine.
Answer: C
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