Problem Solving

Q1: Can someone give me an easy explanation? please? The question is attached. 5 POSSIBLE (A-E) answers are:

2C+30
______
3

2C-30
______
2

C-10
______
3

2C-10
______
3

2C-30
______
3


Q2: Can someone give me an easy explanation? please? Scanning didnt go so well so here is the missing equation:

C = 90 +9/11 (Y)


Thank you so much.

Q1:
Note that C is defined by the question as the total cost of the bagel and coffee, not the cup of coffee itself. Thus, the equation B=2C-30 is wrong: what you should do is denote the coffee as a different variable X, so that B=2x-30, and C(total cost) = B+X = 2x-30+x = 3x-30.
Here comes the confusing part - we want B, not X. Isolate X from the first equation, and plug that into C:
If B=2x-30, then
2x=B+30
X=(B+30) /2

So if C=B+X, then C=(B+30)/2 + B = B+30+2B/2 which is indeed answer choice E.

I agree that this is confusing - I myself am partial to the plugging in approach. But even there you need to be careful not to turn C into "coffee": C is the total price of the bagel and coffee together. If Coffee is 50 cents, then bagel is 30 cents less than twice 50, or 70 cents, and C=Total cost = 70+50 = 120.

Plug in C=120 into the answer choices and eliminate those answer choices which do not equal the price of the bagel=70 cents:




2C+30 = 2*120+30 / 3 = 270/3 = 90 not equal to 70, so we eliminate.
______
3

2C-30 = 2*120-30 / 2 = 210/2 = 105 - not equal to 70, so we eliminate
______
2

C-10 = 120-10 / 3 = 110/3 - this is too small to be 70. Eliminate
______
3

2C-10 = 2*120-10 / 3 = 240-10 / 3 = 230/3 - this is going to be a fraction, and not equal to 70. Eliminate.
______
3

2C-30 = 2*120 - 30/3 = 240-30 / 3 - 210/3 = 70.
______
3

Since this answer choice is the only one that matches your goal of 70 cents for C=120, it must be the right answer choice, and you needn't worry about the algebra.

That C totally got me. Thank you so much.
This is awesome!!!

ithamarsorek wrote:

Q2: Can someone give me an easy explanation? please? Scanning didnt go so well so here is the missing equation:

C = 90 +9/11 (Y)


Thank you so much.

The question is asking what happens to Y when we add 99 million to C. the way the equation is currently constructed, finding this out will be difficult - I would probably take the initial step of isolating Y in terms of C.
C-90 = 9/11 * Y
multiply by 11 and divide by 9 to isolate Y:
(C-90) * 11 / 9 = Y

Now that you have Y as a function of C, plug in for C, find the relevant Y, then add another 99 to C, find the new Y:
Let's say that C originally is 99, so that 99-90 becomes a nice 9 to reduce with the 9 in the denominator.
If C=99, then
(99-90) * 11 / 9 = 9*11/9 = 11 = Y.
So Y is 11.
Now, what happens when we add another 99 to C? C is now 99+99. Plug this into the equation and find the new Y:
(99+99-90) * 11/9 = (99+9) * 11/9 =
You can calculate 99+9 and divide by the 9 in the denominator, but it'll be easier to just extract 9 as a common factor and reduce with the 9 in the denominator: 99+9 is 9(11+1) = 9*12, so
9*12*11 / 9 = 12*11 = 132.
And that is the new Y.
What did the question ask? How much is the increase? From the old Y=11 to the new Y=132, we have an increase of 132-11=121, so the answer is D.

Thanks much!!!
U r the best.