A farmer has 10 tons of watermelons stored in a barn. The

watermelons contain 99% water, by weight. During storage, the

melons dry out so that their water content is decreased to 98% of their

new weight.

What is the weight of the watermelons now?

Printable View

- Sep 30th 2013, 04:19 PMSuperMaruKidWatermelons
A farmer has 10 tons of watermelons stored in a barn. The

watermelons contain 99% water, by weight. During storage, the

melons dry out so that their water content is decreased to 98% of their

new weight.

What is the weight of the watermelons now? - Sep 30th 2013, 06:31 PMHallsofIvyRe: Watermelons
This is pretty much just arithmetic. There are 10 tons of watermelons and the are 99% water. That means they are (10)(.99)= 9.9 tons water, 0.1 tons "non-water". The melons "dry out", losing only water so that their water weight is 98% of their new weight. Let the weight of water lost, in tons, be "w". Then their total weight is 10- w and their water weight is 9.9- w. That is a ratio of $\displaystyle \frac{9.9- w}{10- w}= .98$. Solve for w. The new weight of the water melons is 10- w tons.

- Sep 30th 2013, 09:00 PMvotanRe: Watermelons
- Oct 1st 2013, 05:44 AMHallsofIvyRe: Watermelons
- Oct 1st 2013, 06:03 AMSorobanRe: Watermelons
Hello, SuperMaruKid!

Quote:

A farmer has 10 tons of watermelons stored in a barn.

The watermelons contain 99% water, by weight.

During storage, the melons dry out, so that their water content

is decreased to 98% of their new weight.

What is the weight of the watermelons now?

Originally, the watermelons are 99% water and 1% solids.

The farmer has 20,000 pounds of watermelons

The amount of solids is: $\displaystyle 1\% \times 20,\!000 \:=\:200\text{ pounds.}$

When the melons are reduced to $\displaystyle x$ pounds, they will be 2% solid.

. . $\displaystyle 2\% \times x \:=\:0.02x\text{ pounds}$

The amount of solids remains constant: .$\displaystyle 0.02x \,=\,200$

Therefore: .$\displaystyle 0.02x \:=\:200 \quad\Rightarrow\quad x \:=\:10,\!000\text{ pounds} \:=\:5\text{ tons}$