help please

Question

Jenny was mixing herself a glass of chocolate milk. “You certainly have enough chocolate syrup in the glass,” remarked Kevin, who then found a glass of milk of his own to drink. “Only a third of a glass of syrup, “ said Jenny. “And you’re certainly taking your share.” “I only have one-fourth of a glass,” estimated Kevin. “But Kevin, your glass holds twice as much as mine!” “Tell you what,” said Kevin, after they both had mixed milk and syrup in their glasses. “Let’s combine our drinks in a larger pitcher, and then split the whole amount.” While Jenny is trying to decide whether or not this arrangement is to her advantage, can you say what part of the combined mixture would be syrup? Use pictures, numbers, or words to show your solutio

Answer 1

Let's assume Jenny's glass holds x ml of liquid

 

Thus Kevin's glass holds 2x ml of liquid

 

Jenny's glass holds (x/3) ml of chocolate syrup and (2x/3) ml of milk

 

Kevin's glass has ( 2x/4) 0r (x/2) ml of milk and (2x/3) ml of chocolate syrup

 

The combination of mixtures in the pitcher contains [(x/3)+(2x/3)]  ml of chocolate syrup  from respective glasses of Jenny and Kevin = x ml of chocolate syrup

while the volume of combination is [(x/3)+(2x/3)] of chocolate syrup + (2x/3) ml of milk from Jenny's glass +(x/2) ml of milk from Kevin's glass ={ x+[(4x+3x)/6] } ml = { x+ (7x/6)} ml = (13x/6) ml

 

Hence x ml of (13x/6) ml is chocolate syrup thus (6/13) part of combined mixture will be syrup, or in every 13 ml or any unit of combined mixture 6 part will be syrup

 

Note: since it has not been mentioned how much syrup Kevin added to his one fourth of a glass of milk, I have thought it's one third glass of syrup. Other wise, thinking Kevin added to one fourth glass of milk as much syrup required to create a mixture that is equal in proportion to a mixture with a third of a glass of syrup and two third of glass of milk,  it can be as following: 

 

Let's assume Jenny's glass holds x ml of liquid

Thus Kevin's glass holds 2x ml of liquid

Jenny's glass holds (x/3) ml of chocolate syrup and (2x/3) ml of milk

Kevin's glass has ( 2x/4) or (x/2) ml of milk which is 2/3 rd of mixture, thus he must have added (x/4) ml of syrup as (2/3) of the mixture has a volume of (x/2) ml, (1/3) i.e., half of (2/3) or (1/2) of (2/3) of the mixture must have a volume of (1/2) of (x/2) ml or (x/4) ml

The combination of mixtures in the pitcher contains [(x/3)+(x/4)] ml of chocolate syrup from respective glasses of Jenny and Kevin = [(4x+3x)/12]ml of chocolate syrup = (7x/12)ml of chocolate syrup
while the volume of combination is [(x/3)+(x/4)] of chocolate syrup + (2x/3) ml of milk from Jenny's glass +(x/2) ml of milk from Kevin's glass ={ (7x/12)+[(4x+3x)/6] } ml = {(7x/12)+ (7x/6)} ml = (7x+14x/12) ml =(21x/12) ml

Hence (7x/12) ml of (21x/12) ml is chocolate syrup or (7x/21x) or (1/3) part of combined mixture will be syrup or in every 3 ml or any unit of combined mixture 1 part will be syrup.

 

Post Script: This editor does not support drawing diagrams.