Mr. Young had some bottles of apple juice and orange juice. The ratio of the number of bottles of apple juice to the number of bottles of orange juice was 3:2. After he sold 64 bottles of apple juice, the ratio became 1:6. How many bottles of apple juice and orange juice did Mr. Young have altogether in the end?

A t t h e b e g innin g : 3 x − n u mb er o f b o ttl es o f a ppl e j u i ce 2 x − n u mb er o f b o ttl es o f or an g e j u i ce A f t er s a l e : 1 x − n u mb er o f b o ttl es o f a ppl e j u i ce 6 x − n u mb er o f b o ttl es o f or an g e j u i ce 2 x 3 x − 64 ​ = 6 x 1 x ​ 2 x 3 x − 64 ​ = 6 1 ​ C ross m u lt i pl i c a t i o n : 6 ( 3 x − 64 ) = 2 x 18 x − 384 = 2 x ∣ s u b t r a c t 2 x 16 x − 384 = 0 ∣ a dd 384 16 x = 384 ∣ d i v i d e b y 16 x = 24 He ha d 24 b o ttl es o f a ppl e j u i ce an d 144 o f or an g e j u i ce .

Answered by luana | 2024-06-10

If the ratio of the number of bottles of apple juice to the number of bottles of orange juice was 3:2, then you can denote 3x - the number of bottles of apple juice and 2x - the number of bottles of orange juice.
After he sold 64 bottles of apple juice, the number of bottles of apple juice became 3x-64 and the number of bottles of orange juice remained 2x.
The new ratio is 1:6, this means that
2 x 3 x − 64 ​ = 6 1 ​ .
Solve this equation:
( 3 x − 64 ) ⋅ 6 = 2 x ⋅ 1 , 18 x − 384 = 2 x , 18 x − 2 x = 384 , 16 x = 384 , x = 16 384 ​ = 24.
In the end Mr. Young had:

3 x − 64 = 3 ⋅ 24 − 64 = 8 bottles of apple juce;
2 x = 2 ⋅ 24 = 48 bottles of orange juice.

Answered by frika | 2024-06-24

Mr. Young originally had 72 bottles of apple juice and 48 bottles of orange juice. After selling 64 bottles of apple juice, he has 8 bottles of apple juice left and still 48 bottles of orange juice. In total, he has 56 bottles of juice remaining.
;

Answered by luana | 2024-10-15