For each customer, a bakery charges p dollars for the first loaf of

For each customer, a bakery charges p dollars for the first loaf of bread bought by the customer and charges q dollars for each additional loaf bought by the customer. What is the value of p ?

(1) A customer who buys 2 loaves is charged 10 percent less per loaf than a customer who buys a single loaf:

Price of 2 loaves = $(p+q).
Price per loaf = $(p+q)/2

Price of a single loaf = $p.

Given that (p+q)/2=0.9p.

Two unknowns. Not sufficient.

(2) A customer who buys 6 loaves of bread is charged 10 dollars --> p+5q=10. Not sufficient.

(1)+(2) We have two distinct linear equations with two unknowns: (p+q)/2=0.9p and p+5q=10, thus we can solve for both p and q. Sufficient..

Answer: C.

Hope it's clear.
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Question stem tells you that p $ for 1st loaf and q $ for additional loaf.

1. if someone buys 2 loaf , he will be charged p+q $.
price per laof = (p+q) / 2 $

if one buys only 1 loaf then one pays only p $

St1 tells that

(p+q)/2 = (1-10%) p
p/2+q/2 = 9/10p
q=0.8 p

Cant figure out p insufficient.

2. 6 loaves price is p+5q given as 10$
p+5q=10

Insufficient.

Together 1 & 2
p+5*0.8p = 10
p =2$
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Answer: C

Cost for first loaf = p
Cost for remaining = q

S1: Cost of two loaves = p+q
Price /loaf = (p+q)/2 = 0.9p (10% discount)

p+q = 1.8p

or q = 0.8p

or 4p -5q = 0

Not sufficient.


S2: 10 = p+5q
Not sufficient.

S1 & S2:
p+5q = 10
4p-5q=0

or 5p = 10
p = 2

q = 4x2/5 = 1.6

Sufficient w/ 2 equations.

i cant get the warding of st one...........Help guys

Statement 1 says that when you buy 2 loaves of bread instead of 1, you get a discount of 10% per loaf.

If you buy 2, then the cost is (p+q)
Cost per loaf = (p+q)/2 = 0.5p+0.5q


If you buy 1, the cost is p.
Cost per loaf = p/1 = p

You get a 10% discount per loaf..

i.e. 0.5p+0.5q = 0.9p

or 0.5q = 0.4p

or 5q = 4p

Statement 1 says that when you buy 2 loaves of bread instead of 1, you get a discount of 10% per loaf.

If you buy 2, then the cost is (p+q)
Cost per loaf = (p+q)/2 = 0.5p+0.5q


If you buy 1, the cost is p.
Cost per loaf = p/1 = p

You get a 10% discount per loaf..

i.e. 0.5p+0.5q = 0.9p

or 0.5q = 0.4p

or 5q = 4p

but dont you think that the part in read is the average cost per loaf not cost per loaf

For each customer, a bakery charges p dollars for the first loaf of bread bought by the customer and charges q dollars for each add'l loaf bought by the customer. What's the value of p?
(1) A customer who buys 2 loaves is charged 10% less per loaf than a customer who buys a single loaf.
(2) A customer who buys 6 loaves of bread is charged 10 dollars.

general formula to calculate price

x = p+nq where n is number of loafs in excess of one

from one

original price of two loafs is = p+q

fro one i think it means

p+q = 2(0.9)p = 1.8p

thus 0.8p=q

from two
p+5q = 10

both together

p+5(0.8p) = 10

thus 5p = 10 and p = 2 and q = 1.6

what is my mistake here

I used a combination of math and some guess work.

I have seen these type of problems before and made the mistake of thinking it was E in the past. However this time I knew it was D ...From the two stems it looks like you are going to get two equations with two variables which one can solve. I just made the sure the equations weren't equal to each other when I chose D...I didn't actually work all the way through the problem.

What would be the equations for this question?

Hi

In this why cant the answer be B.

We have the equation, p+5q=10

The only possible value that q can take is 1. Thus, we can get p as 5.

You don't necessarily know that q is an integer. Dollar amounts can be non-integers.

For instance, the first loaf could cost 3.2 dollars, and the remaining 5 loaves could cost 1.36 dollars each. 3.2 + 5(1.36) = 10, which fits statement 2.
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\({\text{\$ }}p\,\,\,:\,\,{\text{first}}\,\,{\text{loaf}}\)

\({\text{\$ }}q\,\,\,{\text{:}}\,\,\,{\text{any}}\,\,{\text{additional}}\,\,{\text{loaf}}\)

\(? = q\)

\(\left( 1 \right)\,\,{\left( {\frac{{\,{\text{charge}}\,}}{{{\text{loaf}}}}} \right)_{\,2\,\,{\text{loaves}}}} = \frac{{p + q}}{2}\,\,\,\,\mathop = \limits^{{\text{given}}} \,\,\frac{9}{{10}}p\,\,\,\,\, \Rightarrow \,\,\,\, \ldots \,\,\,\,\, \Rightarrow \,\,\,\frac{q}{p} = \frac{4}{5}\)

\(\left\{ \begin{gathered}\\
\,{\text{Take}}\,\,\left( {p,q} \right) = \left( {0.5,0.4} \right)\,\,\,\,\, \Rightarrow \,\,\,\,\,? = 0.4 \hfill \\\\
\,{\text{Take}}\,\,\left( {p,q} \right) = \left( {1,0.8} \right)\,\,\,\,\, \Rightarrow \,\,\,\,\,? = 0.8 \hfill \\ \\
\end{gathered} \right.\)

\(\left( 2 \right)\,\,6\,\,{\text{loaves}}\,\,{\text{for}}\,\,\$ 10\,\,\,\left\{ \begin{gathered}\\
\,{\text{Take}}\,\,\left( {p\,;q} \right) = \left( {2\,;\frac{8}{5}} \right)\,\,\,\,\, \Rightarrow \,\,\,\,\,? = \frac{8}{5} \hfill \\\\
\,{\text{Take}}\,\,\left( {p\,;q} \right) = \left( {3\,;\frac{7}{5}} \right)\,\,\,\,\, \Rightarrow \,\,\,\,\,? = \frac{7}{5} \hfill \\ \\
\end{gathered} \right.\)

\(\left( {1 + 2} \right)\,\,\,\left\{ \begin{gathered}\\
p + 5q = 10 \hfill \\\\
\frac{q}{p} = \frac{4}{5} \hfill \\ \\
\end{gathered} \right.\,\,\,\,\,\,\,\mathop \Rightarrow \limits^{{\text{k}}\,\,{\text{technique}}} \,\,\,\,\left( {5k} \right) + 5\left( {4k} \right) = 10\,\,\,\,\, \Rightarrow \,\,\,\,\,? = 4k\,\,{\text{unique}}\,\)


This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
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IMO C.

Both will give equations of 2 variables, and then we can solve to get p.

Hi Bunuel

Can you please help me understand this statement?

(1) A customer who buys 2 loaves is charged 10 percent less per loaf than a customer who buys a single loaf:

Price of 2 loaves = $(p+q).
Price per loaf = $(p+q)/2

Price of a single loaf = $p.

As per my understanding p+q = 1p -10%p which will be p+q = 0.9p

But unable to understand where is (p+q)/2 coming from?

Say bakery charges 2 dollars for the first loaf of bread bought by the customer and charges 1.6 dollars for each additional loaf bought by the customer.

If you buy 2 loaves, you pa $2 + $1.6 = $3.6, so ($2 + $1.6)/2 = $3.6/2 = $1.8 per loaf, which is 10 percent less per loaf than a customer who buys a single loaf for $2 ($1.8 = 0.9*$2).
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Thank you Bunuel. I was getting confused because of consideration about avg and single loaf price as same.

Can you please link me with any thread to connect for similar type of sums?

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