What is the cost of the bicycle?

Question

Brian and his brother Matt both want to buy the same model bicycle. Brian needs $73 more before he can afford the bike. Matt needs $65 more. If they combine their money, they will have just enough to buy one bicycle that they could share. What is the cost of the bicycle?

Answer 1

If Matt gives what he has to Brian, Brian can buy the bike. So Matt has $73.

Is Brian gives what he has to Matt, then Matt can buy the bike. So Brian has $65

If they combine what they have, $138, they can buy the one bike.

QED

Answer 2

Let x be the cost of the bike. Since Brian needs $73 more to buy the bike that means he got only x-73 money. Similar Matt has x-65 money. When they combine their money they get (x-73)+(x-65) which is same as the cost of one bike x.

Therefore (x-73)+(x-65)=x

Solving for x:

x-73+x-65=x

x-138=0

or x=138

Bike cost $138

Answer 3

Cost = C

B = C-73

M=C-65

B+M =C

B+C-65 =C

B =65

C-73+M = C

M=73

C =65+73 = $138

Answer 4

Let the cost of the bike be called x.

Brian needs $73 more than the cost of the bike, so he has $(x - 73).

Matt needs $65 more than the cost of the bike, so he has $(x - 65).

If they combine their money, they will have exactly enough to buy a single bike, so we can say:

(Brian's money) + (Matt's money) = The cost of the bike

(x - 73) + (x - 65) = x

2x - 138 = x

x = 138