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?

Guest Jan 20, 2020

#1**+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.

Badada Jan 20, 2020

#2**+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

ElectricPavlov Jan 21, 2020

#3**+1 **

~~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

GingerAle Jan 21, 2020

#5**+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

Dragan
Jan 22, 2020