SOLUTION: Jessica, Mary and Alice share a tin of beans in the ratio 4:5:6 and a portion of peas in the ratio 5:3:4. Alice's helping of beans is three times as big as her helping of peas.

Question 446459: Jessica, Mary and Alice share a tin of beans in the ratio 4:5:6 and a portion of peas in the ratio 5:3:4. Alice's helping of beans is three times as big as her helping of peas.
1) Show clearly that the ratio of the size of the tin of beans to the size of the portion of peas is 5:2
2)What is the ratio of the sizes of Mary's helpings of beans and peas?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Jessica, Mary and Alice share a tin of beans in the ratio 4:5:6 and a portion of peas in the ratio 5:3:4.
Alice's helping of beans is three times as big as her helping of peas.
;
Let x Bean multiplier
Let y Peas multiplier
then
J, M, A Beans: 4x, 5x, 6x
J, M, A Peas: 5y, 3y, 4y
:
"Alice's helping of beans is three times as big as her helping of peas."
6x = 3(4y)
6x = 12y
x = 2y
:
1) Show clearly that the ratio of the size of the tin of beans to the size of the portion of peas is 5:2
Beans: 4x + 5x + 6x = 16x is the amt of beans
Replace x with 2y, find amt of beans in terms of y:
then: 8y + 10y + 12y = 30y is the amt of beans
:
Peas: 5y + 3y + 4y = 12y is the amt of peas
:
Ratio of Beans to Peas: 30:12 which is 5:2
:
;
2)What is the ratio of the sizes of Mary's helpings of beans and peas?
Mary's beans: 5x,
Mary's peas: 3y
replace x with 2y
10y:3y, 10:3 is Mary's helpings of beans and peas

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