Question

two sisters were walking along the beach collecting shells. after 30 minutes, they had collected shells in a ratio of 3:2, with the older sister having collected more than the younger. because the older one had more shells, the younger sister began to cry. to make her feel better, the older sister gave her sibling 11 of her own shells. as a result, the new ratio of shells between the older and younger sister was now 2:5. how many shells did the younger sister then have?

Answer 1

younger sister now has 25 shells

Explanation:

given the shells in the ratio older : younger = 3 : 2 = 3n : 2n ( n is a multiplier )

the older sister gives 11 shells to younger sister , then

older sister has 3n - 11 shells

younger sister has 2n + 11 shells

given the ratio is now 2 : 5 , the expressing theratio as a fraction

`(3n-11)/(2n+11)` =
`(2)/(5)` ( cross- multiply )

5(3n - 11) = 2(2n + 11) ← distribute parenthesis

15n - 55 = 4n + 22 ( subtract 4n from both sides )

11n - 55 = 22 ( add 55 to both sides )

11n = 77 ( divide both sides by 11 )

n = 7

Then younger sister has 2n + 11 = 2(7) + 11 = 14 + 11 = 25 shells