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# Did You Find Out? Get the Answer to the Riddle of E-News Issue No. 2, April 2018

2018-03-27

## How Many Branches Are They Carrying? Max, Tim, and Laura are stranded on an island. They collect branches in order to make a campfire. Max has collected the most. If he dropped 10 branches, he would have as many as Tim. If Laura dropped 10, she would only have 1/5 as many as Max. And if Tim took 5 branches from Laura, he would have exactly twice as many as her.

How many branches does each one carry to the campfire?

## Solution

Based on the information provided, it is possible to make three equations with the following variables:
x = Max
y = Tim
z = Laura

 I. x-10 = y -> x = y+10 II. z-10 = 1/5x -> z = 1/5 x + 10 -> z = 1/5(y+10)+10 -> z = 1/5 y+12 III. y+5 = 2(z-5) -> y = 2z-15

After solving the equations for x, y, and z, you can plug the solutions into the other equations. Plug the solution for x from equation I into equation II and so on.

 in III.) y = 2( 1/5y+12) -15 Solve the equation for the remaining unknown variable. y = 2/5y + 9 Plug the result for y into equation I, and the result for x into equation II. 3/5y = 9 y = 15 in I.) x-10 = 15 x = 25 in II.) z-10 = 1/5 * 25 z = 15

The solution is that Max is carrying 25 branches, and Tim and Laura are each carrying 15.

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