Question

Coffee A and coffee B are mixed in the ratio x:y by weight. A costs $50/kg and B costs $40/kg. If the cost of A is increased by 10% while that of B is decreased by 15%, the cost of the mixture per kg remains unchanged. Find x:y.

Answer 1

@Callisto @zzr0ck3r @hartnn @Fifciol

Answer 2

@terenzreignz

Answer 3

Word problems are generally simple as far as solving goes, the tricky part is setting up what to solve... so let's see...

Answer 4

Okay, so, coffee A costs 50 per kg, and there are x kilograms of coffee A...
coffee B costs 40 per kg, and there are y kilograms of coffee B...
so we have
50x + 40y = k
Where k is the cost...

Answer 5

k is the cost of the mixture....
catch me so far?

Answer 6

yes

Answer 7

So, if we increase the cost of x by 10%... what is its new price per kg?

Answer 8

lol... @kryton1212 you better make your presence felt :P

Answer 9

1.1x ...

Answer 10

okay, so what is 1.1*50?

Answer 11

55...

Answer 12

That's correct, so that's the new price of coffee A.
What about coffee B?
We *decrease* its cost by 15% so what is its new price?

Answer 13

55x+34y=k?

Answer 14

Yes, that is correct :)
And since we have
50x + 40y = k
and
55x + 34y = k

then clearly
50x + 40y = 55x + 34y

Answer 15

Can you take it from there? :)

Answer 16

yes,
5x=6y

Answer 17

6:5

Answer 18

Good job ^_^

Answer 19

thanks:))