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Alice and Bob share an allotment. The ratio of the area of Alice's
portion to the area of Bob's portion is 3:2. They each grow
vegetables and fruit on the allotment. The entire allotment is
covered by vegetables and fruit in the ratio 7:3. On Alice's
portion of the allotment, the ratio of vegetables to fruit is 4:1
What is the ratio of vegetables to fruit in Bob's portion?​

Respuesta :

ZJSG09112007

Answer:

11:39

Step-by-step explanation:

Bob's portion of the allotment :

[tex]Total\:ratio=3+2 =5\\\\= \frac{2}{5}[/tex]

Alice's portion :

[tex]Total\:ratio=3+2 =5\\\\= \frac{3}{5}[/tex]

Vegetables are :

[tex]Total\:ratio=7+3 =10\\\\= \frac{7}{10}[/tex] of the total area

Vegetables are :

[tex]Total\:ratio=4+1 =5\\\\= \frac{4}{5}[/tex] of Alice's portion, or:

[tex]\frac{4}{5} \times(\frac{3}{5} ) = \frac{12}{25}[/tex]

Bob's portion fraction (b):

[tex]\frac{12}{25} + b = \frac{7}{10}[/tex]

L.C.M of 25 and 10 =50

[tex]\frac{24}{50} + b = \frac{35}{50} \\\\b =\frac{11}{50}\\\\ Ratio:\\50 - 11 = 39[/tex]

Bob's vegetable to fruit ratio is 11 : 39

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