A woman sold 100 oranges at $12.10, some at the rate of 3

Question

A woman sold 100 oranges at $12.10, some at the rate of 3 for 35 cents and the rest at 7 for 85 cents. How many were sold at the first rate?

A. 45
B. 21
C. 9
D. 15
E. 12

stanford2012 · Accepted Answer

This can be solved like a classical mixture problem but numbers are awkward to deal with.

It's easier to just look at the answer choices. You know that a multiple of 3 oranges has to be sold at the first rate, and a multiple of 7 at the second rate. You simple subtract the answer choices for the first rate from 100 and check whether the remainder (i.e. the number of oranges sold at the second rate) is a multiple of 7.

100 - 45 = 55 => not a multiple of 7 so exclude
100 - 21 = 79 => not a multiple of 7 so exclude
100 -9 = 91 => a multiple of 7 so keep
100 - 15 = 85 => not a multiple of 7 so exclude
100 - 12 = 88 => not a multiple of 7 so exclude

Hence, answer choice 9 is correct.

MBAhereIcome · Answer

\frac{35}{3}x+\frac{85}{7}(100-x)=1210

solve and you'll get x = 9

GMATD11 · Answer

\frac{35}{3}x+\frac{85}{7}(100-x)=  1210  
 
Can you pls explain the Right hand side of equation.
Won't it be 12.10

KarishmaB · Answer

The equation equates the total selling price. He gets $12.10 i.e. 1210  cents .
If he sold x oranges for 35/3 cents and (100-x) for 85/7 cents, this is a total of 
(35/3) * x + (85/7) * (100-x)  cents . You equate cents to cents.

Also, you can use the weighted average formula here:

w1/w2 = (85/7 - 121/10)/(121/10 - 35/3) = 9/91

Total 9+91 is 100. So he sells 9 oranges at 35 for 3 and 91 oranges at 85 for 7.

Versatile720 · Answer

Hi,

Because we are taking all the values in cents so we have converted $12.10 into cents which is 1210 cents.
as 1 cent =0.01 Dollar

Hope this helps.

Try and fail but never fail to try.

ankur1901 · Answer

for such question need a will power to take on some random complicated numbers. i derived the equation but goofed up with the numbers

shriramvelamuri · Answer

simple question.... killer calculation.. WOW...

Prowess · Answer

Let quantity of 35 cent be X and for 85 cent be Y. So X should be multiple of 3 and Y be 7 respectively. 
C. X-9, Y-91 the only option satisfies the condition.

Posted from my mobile device

LeenaPG · Answer

Solution :

3 oranges sold for 35 would be 35/3 and 7 for 85 would be 85/7.

now forming the equation:

35/3*x + 85/7*y = 1210 cents

x+y = 100

Now substitute the values for x from the answers given.

all the choices given are multiples of 3 - so we know 35/3*x would be integer.

Check the second one 85/7 * (100 - x)

Only when x=9 , y = 91 which is divisible by 7.

So Answer = C

bumpbot · Answer

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A woman sold 100 oranges at $12.10, some at the rate of 3

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