SOLUTION: please help me solve this word equation with full working out. ben and vickky have $250 between them. ben gives Vickky $50. now vickky has 4 times as much money as Ben. use an

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: please help me solve this word equation with full working out. ben and vickky have $250 between them. ben gives Vickky $50. now vickky has 4 times as much money as Ben. use an       Log On


   

Question 421484: please help me solve this word equation with full working out.
ben and vickky have $250 between them. ben gives Vickky $50. now vickky has 4 times as much money as Ben. use an equation to find out how much money each of them had to start with.
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
b equals amount of money that ben has.
v equals amount of money that vickie has.

b + v = $250.00

ben give vickie $50.

ben is left with b - 50
vickie is left with v + 50

now vickie has 4 times as much money as ben has.

this leads to the equation of:

v + 50 = 4 * (b-50)

you have 2 equations that need to be solved simultaneously.

they are:

b + v = 250
v + 50 = 4 * (b - 50)

you can use the first equation to solve for v or b. we'll solve for b.

we get b = 250 - v

you can then substitute for b in the second equation to get:

v + 50 = 4 * (b - 50) becomes:

v + 50 = 4 * (250 - v - 50)

combine like terms to get:

v + 50 = 4 * (200 - v)

perform indicated operations to get:

v + 50 = 800 - 4*v

add 4*v to both sides of the equation and subtract 50 from both sides of the equation to get:

v + 4*v = 800 - 50

combine like terms to get:

5*v = 750

divide both sides of the equation by 5 to get:

v = 150

since b + v = 250, this means that b = 100

we have b = 100 and v = 150

this satisfies b + v = 250

we also need to satisfy v + 50 = 4 * (b-50)

substitute in this equation to get:

150 + 50 = 4 * (100 - 50)

perform indicated operations to get:

200 = 4 * 50 which becomes 200 = 200 which is true.

looks looks like the values for b and v are good.

answer is:

ben starts off with 100 dollars and vickie starts off with 150 dollars.

ben give vickie 50 dollars.

ben now has 50 dollars and vickie has 200 dollars.

vickie now has 4 times the money that ben has.