Rasheed bought two kinds of candy bars

[haoyang_qu]

Rasheed bought two kinds of candy bars, chocolate and toffee, that came in packages of 2 bars each. He handed out 2/3 of the chocolate bars and 3/5 of the toffee bars. How many packages of chocolates bars did Rasheed buy?

(1) Rasheed bought 1 fewer packages of chocolate bars than toffe bars.

(2) Rasheed handed out the same number of each kind of candy bar.


x = the number of chocolate bars that Rasheed bought
y = the number of toffee bars that Rasheed bought

2/3 x is the number of chocolate bars that he handed out
3/5y is the number of toffee bars that he handed out

Total number of candy bars bought = x + y

(1) x = y - 1
T = (y - 1) + y

not enough info

(2) 2/3 x = 3/5 y

not enough info

together: I don't see how the two statements together are sufficient.
If you substitute the info in statement 2, it still isn't sufficient info.
What am I missing?
Thanks.

[priyankur.saha]

1. 1 fewer packages so first equation should be x/2 = y/2 - 1
2. (2/3)x = (3/5)y

Plug value of x from second equation to first equation and find y. Do not consider any outside information.
from 2: x = 9/10 y
after plug in, from 1: 9/10 *y/2 = y/2 - 1 .... solve it.

So C is suffice.

[haoyang_qu]

Thanks.
Can you explain your equation from statement 1 more?

[priyankur.saha]

Sure, here it goes...
Rasheed bought two kinds of candy bars, chocolate and toffee, that came in packages of 2 bars each. He handed out 2/3 of the chocolate bars and 3/5 of the toffee bars. How many packages of chocolates bars did Rasheed buy?

(1) Rasheed bought 1 fewer packages of chocolate bars than toffe bars.

(2) Rasheed handed out the same number of each kind of candy bar.

x = the number of chocolate bars that Rasheed bought
So number of packages = x/2
y = the number of toffee bars that Rasheed bought
number of packages = y/2

(1) Rasheed bought 1 fewer packages of chocolate bars than toffe bars.
-- equation should be x/2 = y/2 -1

[RonPurewal]

this works.

but,
here's a way that's probably easier:
let the variables stand for the numbers of packages.

two reasons to do this instead:
(a) the prompt question is stated in terms of a number of packages, not a number of bars. (this is a simple matter of rephrasing, and is thus no big deal, but it's still worth noting.)
(b) you won't have to deal with quite as many fractions.

let C = # of packages of chocolate bars
let T = # of packages of toffee bars
therefore
2C = # of chocolate bars
2T = # of toffee bars

then
statement (1) says C = T - 1
statement (2) says (2/3)(2C) = (3/5)(2T), or, 4C/3 = 6T/5

substitution works here, too.

--

also, it's a MUCH better idea to use "C" and "T" than to use "x" and "y".
the more transparent your notation, the faster you'll solve the problem, and the lower the chance of your making a mistake.
when you're under time pressure and test anxiety, the last thing you'll want to do is waste a bunch of time reminding yourself which one is "x" and which one is "y". IT IS MUCH EASIER THAN YOU MIGHT THINK TO CONFUSE THESE THINGS, ESPECIALLY UNDER EXAM PRESSURE.

[ashish.jere]

thanks.

this works.

but,
here's a way that's probably easier:
let the variables stand for the numbers of packages.

two reasons to do this instead:
(a) the prompt question is stated in terms of a number of packages, not a number of bars. (this is a simple matter of rephrasing, and is thus no big deal, but it's still worth noting.)
(b) you won't have to deal with quite as many fractions.

let C = # of packages of chocolate bars
let T = # of packages of toffee bars
therefore
2C = # of chocolate bars
2T = # of toffee bars

then
statement (1) says C = T - 1
statement (2) says (2/3)(2C) = (3/5)(2T), or, 4C/3 = 6T/5

substitution works here, too.

--

also, it's a MUCH better idea to use "C" and "T" than to use "x" and "y".
the more transparent your notation, the faster you'll solve the problem, and the lower the chance of your making a mistake.
when you're under time pressure and test anxiety, the last thing you'll want to do is waste a bunch of time reminding yourself which one is "x" and which one is "y". IT IS MUCH EASIER THAN YOU MIGHT THINK TO CONFUSE THESE THINGS, ESPECIALLY UNDER EXAM PRESSURE.

[Ben Ku]

I'm glad that was helpful.