# A group of three friends ate dinner at a restaurent. when they settled the check,peter paid 4/5 as much as?

A group of three friends ate dinner at a restaurant. when they settled the check,peter paid 4/5 as much as john paid,and john paid 1/3 as much as Ralph paid. what fraction of the check did john pay.

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• David
Lv 7
9 years ago

P + J + R = 1

P = (4/5)J

P = 4J / 5

J = (1/3)R

J = R/3

3J = R

(4J / 5) + J + 3J = 1

(4J / 5) + 4J = 1

(4J + 20J) / 5 = 1

24J = 5

J = 5/24

P = 1/6

R = 15/24 = 5/8

• 9 years ago

lets assume that ralph paid X \$

then John paid 1/3*X

and Peter paid 4/5*1/3*X= (4/15)*X

Now for simplicity sake lets assume their bill was 100\$

therefore the sum paid by the 3 friends should equal 1

therefore X + ((1/3)*X)+ ((4/15)*X) = 1

thus, X(1+1/3+4/15)=1

then, X(24/15)=1

therefore X = 15/24

Now john paid 1/3* X

i.e. (1/3)*(15/24)

= 5/24

John paid 5/24th of the bill

• Pranil
Lv 7
9 years ago

peter = 4/5 john

john = 1/3 Ralph

Ralph = 3 john

peter + john + Ralph = 1

4/5 john + john + 3 john = 1

4/5 john + 4 john = 1

24/5 john = 1

john = 5/24

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• None
Lv 7
9 years ago

P = (4/5)J = (4/15) R

J = (1/3)R

P + J + R = (4/15)R + (1/3)R + R = (24/15)R

J = (1/3)R/(24/15)R = 15/72 = 5/24 of the total