+0

# word problem

0
147
3
+525

John weighed the pumpkins two at a time. After he is done weighing the pumpkins he observed the following weights: 110, 112, 113, 114, 115, 116, 117, 118, 120, and 121 pounds.
How much did each pumpkin weigh?
Explain Clearly how you got the answer?

waffles  Nov 2, 2017
Sort:

#1
+82752
0

Note:

I think this problem is a variation on this theme :

http://web2.0calc.com/questions/how-much-do-they-weigh

CPhill  Nov 2, 2017
#2
+82752
+2

Here's my solution :

I'm assuming that we have 5 pumpkins and we are weighing them in couples and all the pumpkins are of different weights

Let  a > b > c > c > d > e       where these are the weights of the pumpkins

And  each is weighed 4 times.....

So we have that     ( sum of the weights)/4  = 1156/4  ⇒  a + b + c + d + e   = 289

And here are the equations that we are sure of

The two heaviest  = a + b  = 121  (1)

Since a > b, then a + c > b + c....so a + c is the second heaviest weight

a + c  =  120  (2)

The two lightest =  d + e  =  110   (3)

Since c > d, then c + e >  d + e  ......so c + e is the second lightest weight

c + e  =  112  (4)

Subtract  (2) from (1)  =  b - c  = 1  ⇒  b  = c + 1

Subtract  (4) from (3)  =  c - d  = 2  ⇒  c  =  d + 2

So this implies that   b =  d + 3

2a + b + c  =  241   ⇒   b + c    = 241 - 2a  ⇒  (d + 3) + (d + 2)  = 241 - 2a  ⇒

2d + 5  = 241 - 2a    →  2a + 2d  = 236  ⇒  a + d  = 118  ⇒  a = 118 - d

Similarly.....add (3) + (4)  and we have that

c + d  + 2e  =  222  ⇒  (d + 2) + d =  222 - 2e ⇒  2d = 220 - 2e ⇒ d = 110 - e ⇒ e = 110 - d

So

a + b + c + d + e  = 289    and substituitng, we have

(118 - d) + (d + 3) + (d + 2)  + d + (110 - d)  = 289

d + 233  =  289

d = 56 lbs

So

a = 118 - d  =  62 lbs

b = d + 3 =  59 lbs

c = d + 2  =  58 lbs

d = 56 lbs

e = 110 - d = 54 lbs

CPhill  Nov 2, 2017
#3
+18948
+2

John weighed the pumpkins two at a time. After he is done weighing the pumpkins he observed the following weights:

110, 112, 113, 114, 115, 116, 117, 118, 120, and 121 pounds
How much did each pumpkin weigh?
Explain Clearly how you got the answer?

heureka  Nov 2, 2017

### 31 Online Users

We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details