Thread: Algebraic equation

Albert and Bob are on a hiking trip. Each is carrying a pack. If Albert were to take enough of Bob's stuff to increase the weight of his own pack by a third, he would have half of the combined weight inside both packs. If Bob were to take 3 pounds of Albert's stuff, he'd have three-quarters of the combined weight. How much weight is each man carrying?

Originally Posted by pantera

Albert and Bob are on a hiking trip. Each is carrying a pack. If Albert were to take enough of Bob's stuff to increase the weight of his own pack by a third, he would have half of the combined weight inside both packs. If Bob were to take 3 pounds of Albert's stuff, he'd have three-quarters of the combined weight. How much weight is each man carrying?

A good start will be to pick variables for each man's original weight. Let's say you've picked A and B for this.

a) Write an expression, in terms of these variables, representing the combined weight.

b) Write an expression, in terms of (a), for half the combined weight.

c) Write an expression, in terms of A, for one-third of Albert's weight.

d) Write an expression, in terms of A and (c), for Albert's weight after the first hypothetical transfer.

e) Write an equation, in terms of (b) and (d), for the first hypothetical relationship.

f) Write an expression, in terms of B, for Bob's weight after adding three pounds.

g) Write an expression, in terms of (a), for three-fourths of the combined weight.

h) Create an equation, in terms of (f) and (g), for the second hypothetical relationship.

You now have two equations in two unknowns.

i) Solve the system of equations.

If you get stuck, please reply showing your work for the steps you could complete or attempt. Thank you!