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.
;
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