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?
+367 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.
+36916 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
+2440 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
+1486 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 
