At the beginning of a camping trip, a group had 5 bottles, each filled

Question

At the beginning of a camping trip, a group had 5 bottles, each filled with 750 milliliters of water and 15 smaller bottles, each filled with 500 milliliters of water. If 9 of these bottles were used during the trip and the total volume of water left in the remaining bottles was 6,000 milliliters, then the number of used bottles that had 500 milliliters of water was

(A) 2
(B) 3
(C) 5
(D) 6
(E) 9

(A) 2
(B) 3
(C) 5
(D) 6
(E) 9

stne · Accepted Answer

Total volume of water  = 11250 
Remaining  = 6000

Hence consumed  = 11250-6000= 5250

x+y=9 
 750x+500y= 5250

Two distinct equations with two unknowns.We can solve for  y.

y = 6

Ans D

Hope it helped.

siddhantvarma · Answer

OA:
 
Let the number of unused bottles filled with 750 milliliters of water be X. 
Then the number of used bottles filled with 750 milliliters of water = 5 – X 
Let the number of unused bottles filled with 500 milliliters of water be Y. 
Then the number of used bottles filled with 500 milliliters of water = 15 – Y

We need to determine the value of 15 – Y.

Since 9 of these bottles were used during the trip; 
5 – X + 15 – Y = 9 
20 – (X + Y) = 9 
X + Y = 11 (Equation I)

Since the total volume of water left in the remaining bottles was 6,000 milliliters; 
750X + 500Y = 6,000 
75X + 50Y = 600 (Equation II)

Multiplying Equation I by 75 and then subtracting it from Equation II, we get: 
(75X + 50Y) – (75X + 75Y) = 600 – 825 
–25Y = –225 
Y = 9

The number of used bottles that had 500 milliliters of water = 15 – Y = 15 – 9 = 6

D is the correct answer choice.

SwapnilBangera · Answer

5 large bottles of 750 ml
15 small bottles of 500 ml
Total bottles = 5+15=20

9 bottles were used
Remaining 11 bottles had 6,000 ml of water in total

We need to find how many of the 9 used bottles were 500 ml bottles.

x = number of used small bottles (500 ml)
Then 9−x = number of used large bottles (750 ml)

So among the remaining 11 bottles:
Small bottles left = 15−x
Large bottles left = 5−(9−x)=x−4
(That is: total large = 5, used = 9 − x ⇒ remaining = 5 − (9 − x) = x − 4)

Water left:
From remaining small bottles: 
(15−x)×500

From remaining large bottles: 
(x−4)×750

So:
(15−x)⋅500+(x−4)⋅750=6000
7500−500x+750x−3000=6000
(7500−3000)+(250x)=6000
4500+250x=6000
250x=1500
x=6

steffe440 · Answer

The remaining bottles are 11 in total with a total of 6000 ml remaining, if all were small then it would only fit 11*500 =5 500 ml, which is too small. Notice however as soon as we switch from one small to one large we gain 250 ml.

we are now short of 500ml but if we swap 2 small bottles against 2 large bottles, we get 6000ml, hence what remains are 9 small bottles and 2 big bottles.

15 small bottles and 9 remains, hence 6 small bottles were used.

At the beginning of a camping trip, a group had 5 bottles, each filled

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At the beginning of a camping trip, a group had 5 bottles, each filled

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