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?
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.