SOLUTION: Sally and Sue are twins who keep pennies in a tin box. On Monday morning, Sally puts 10 pennies into the box; but on Monday afternoon, Sue takes out half the number of pennies in t

Question 1033273: Sally and Sue are twins who keep pennies in a tin box. On Monday morning, Sally puts 10 pennies into the box; but on Monday afternoon, Sue takes out half the number of pennies in the box. On Tuesday morning, Sally puts another 10 pennies into the box; but on Tuesday afternoon, Sue takes out half the pennies in the box. On Wednesday morning, Sally outs in 10 more pennies; and in the afternoon, Sue takes out a dollar's worth of pennies. If this left 65 pennies in the box, how many pennies were there originally?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the trick here is work your way back from 65 once you figured out what was left in the box.

let x equal the number of pennies originally in the box.
sally puts 10 pennies into the box on monday morning.
the box now contains x + 10 pennies.

sue takes out half the pennies from the box on monday afternoon.
sue takes out (x+10)/2.
pennies left in the box are (x+10)/2.

sally puts another 10 pennies into the box on tuesday morning.
the box now contains (x+10)/2 + 10.
it's a good idea to simplify this at this point in time.
the box contains (x+10)/2 + 20/2 = (x+30)/2.

sue take out half the pennies from the box on tuesday afternoon.
sue takes out ((x+30)/2)/2 = (x+30)/4.
what is left in the box is (x+30)/4.

the number of pennies left in the box is 65.
this means that (x+30)/4 = 65
multiply both sides of this equation to get x+30 = 260.
subtract 30 from both sides of this equation to get x = 230.

there must have been 230 pennies in the box originally.
sally puts in 10 to get 240 on monday morning.
sue takes out half to leave 120 on monday afternoon.
sally puts in another 10 to get 130 on tuesday morning.
sue take out half to leave 65 on tuesday afternoon.

solution looks good.
the number of pennies in the box originally is equal to x which is equal to 230.

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