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Suppose that you have an enormous grapefruit that is 92% water (by weight). The grapefruit weights 100 pounds. If the water content of the grapefruit evaporates until it is 90% water (by weight), then approximately how much does the grapefruit now weigh?

 Jan 20, 2020
 #1
avatar+352 
+4

Let X be the starting weight of the grapefruit, which is 100 pounds. Let W be the amount of water evaporated. Let the amount of water at start be A. 92% of X is A, and 90% of X-W is A - W. Equation is 23X/25 = A, 9(X-W) /10 = A - W. The first equation is 23X = 25A, the second is expanded into 9X-9W = 10A - 10W, or 9X + W = 10A. Remember that we want to find X - W, so we substitute A for X using the first equation. (5/2)(9X + W) =23X.

45X/2 + 5W/2 = 23X. 45X + 5W = 46X. X = 5W. We know X was 100, so 5W = 100, or W = 20. Thus, the final answer is 100-20 = 80. We can check the answer by seeing 90% of 80 is 9/10 * 80 = 72, which is 20 less than 92% of the start.

 Jan 20, 2020
 #2
avatar+20401 
+4

92% water weight   means 8 % grapefruit meat  (or 8 pounds)

At 90% water weight    10% is meat

 

10% x = 8

.1x=8

x= 80 pounds

 Jan 21, 2020
 #3
avatar+1841 
0

The two solutions presented above are wrong.

Apologies:  I’m so use to seeing wrong answers, and the large drop in the x value (weight) are common for these types of questions;

I failed to check and verify my own work. 

 

These types of questions require careful reading to understand what it is asking for. 

 Such questions are common in science and statistics, both in academics and in the real-world.  

The mathematical solution seems paradoxical, but it’s not; it’s the language of the question that gives this illusion. Banana Paradox

\( {\text { Deleted Equation }}\)

\(\text { Here’s the correct equation. }\\ x=8+\dfrac{90}{100}x\\ x=80.0 \;Lbs\\ \text { The weight of the grapefruit is $80.0$ Lbs } \)

This now agrees with Badada’s and EP’s solutions above, and Dragan’s solution below.

 

 

Related question, with an expanded solution method.

https://web2.0calc.com/questions/help-asap-thanks_2#r5

 

 

 

GA

 Jan 21, 2020
edited by GingerAle  Jan 22, 2020
 #5
avatar+378 
+2

Suppose that you have an enormous grapefruit that is 92% water (by weight). The grapefruit weights 100 pounds. If the water content of the grapefruit evaporates until it is 90% water (by weight), then approximately how much does the grapefruit now weigh?

Sorry to say,but you're wrong!

You were correct in this:>   https://web2.0calc.com/questions/help-asap-thanks_2#r5

I'm gonna use the same calculations for this math problem.

 

[ 0.92 * 100 - 0.90 (100 - x)] = x      ( "x" represents the weight loss)

92 - ( 90 - 0.90x) = x

92 - 90 + 0.90x = x

2 + 0.90x = x

2 + 0.90x - 0.90x = x - 0.90x

2 = 0.1x

x = 20

New weight is    100 - x = 80  indecision

Dragan  Jan 22, 2020
edited by Dragan  Jan 22, 2020
 #6
avatar+1841 
0

You are right Dragan! Good work!

I corrected my fuckuplaugh

 

GA

GingerAle  Jan 22, 2020

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