Bob and Betty
"You remember I had bought little Tom, a bat and two balls just last week," said Betty to her husband.
"Yes," said Bob, "we had gone together to the market that day."
"Oh! Ofcourse," exclaimed Betty, "Now Tom has sold them to Bunny. He made 20 percent on the bat but has given away the balls, for which we had paid half as much as the bats, at a loss of 20 percent."
"But, mom, you are forgetting that the balls were worn out," interrupted little Tom. "One could not have made profit on them. Anyhow, I made two dollars on the whole and that should not be too bad."
"Well done, son," said Bob; "business will be your line, when you are young."
How much had Betty paid for the bat and for each ball ?
"Yes," said Bob, "we had gone together to the market that day."
"Oh! Ofcourse," exclaimed Betty, "Now Tom has sold them to Bunny. He made 20 percent on the bat but has given away the balls, for which we had paid half as much as the bats, at a loss of 20 percent."
"But, mom, you are forgetting that the balls were worn out," interrupted little Tom. "One could not have made profit on them. Anyhow, I made two dollars on the whole and that should not be too bad."
"Well done, son," said Bob; "business will be your line, when you are young."
How much had Betty paid for the bat and for each ball ?
Labels: friday special, mathemagic, puzzle
posted by Rajesh Lal at
8:05 AM
14 Comments:
They bought one bat and two balls.
(i) buy = bat + ball * 2
He earned 2$ by selling the stuff.
(ii) sell = buy + 2$
He sold the bat, and made 20% profit (balls were free).
(iii) sell = bat * 1.2
He would have gained 20% more, if he hadn't given the balls away for free.
(iv) sell * 1.2 = sell + ball * 2
Transfrom (i) a tad, then insert (ii) then (iii):
bat = buy - ball * 2 = sell - 2$ - ball * 2 = bat * 1.2 - 2$ - ball * 2
And transform it a bit.
bat * 1.2 - bat = ball * 2 + 2$
bat * 0.2 = ball * 2 + 2$ (*)
Insert (iii) in (iv).
(bat * 1.2) * 1.2 = bat * 1.2 + ball * 2
Simplify.
bat * 1.44 - bat * 1.2 = ball * 2
bat * 0.24 = ball * 2 (**)
Insert (**) in (*):
bat * 0.2 = bat * 0.24 + 2$
Simplify again.
bat * 0.2 - bat * 0.24 = 2$
bat * 0.04 = -2$
Et voila:
bat = -2$ * 100 / 4 = -50$ (***)
Transform (*) a bit and insert (***):
bat * 0.2 = ball * 2 + 2$
ball * 2 = -50$ * 0.2 - 2$ = -10$ - 2$ = -12$
Therefore the bat would have cost 50$ and the balls 12$ (so 6$ per ball).
cost of bat = x
cost of a ball = y
original overall cost = x + 2y
sold for value of 1.2x + 1.6y
2 dollar profit made:
x + 2y + 2 = 1.2x + 1.6y
bat is worth twice as much as 2 balls i.e. x = 4y.
4y + 2y + 2 = 4.8y + 1.6y
2 = 0.4y
y = 5
x = 20
to check this: original cost of bat and 2 balls is 20 + 5 + 5 = $30. the bat was sold at a 20% profit, $24, and the balls at a 20% loss, $4 each. overall they were sold for 24 + 4 + 4 = $32 = a $2 profit.
correct values are bat = $20; ball = $5
I agree with Joe
Nice algebra Joe! But the first comment, yours is too elaborate and the mistake is in ur 2nd step of your after giving names, and you should check your math, joe kept it simple and easy for any middle schooler to understand good work
Im not sure joe, you lost me there at some point!
1) where does the 1.6 in 1.6 y come from?
2) didnt tom GIVE Bunny the balls fro free since they were worn out? so how can he have sold them for 4$ each?
thats all!
though like someone else said, i like your algebra! :)
x=cp of bat y=sp of balls
x/5+x=sp of bat =6x/5
y-y/5=sp of balls =4y/5
4y/5 + 6x/5 = 2
y=x/2 given
4/5*4/2
=8x/5 =2
x=10/8
x=5/4
x=1.25$
Bat Cost = x
Bat Selling Price = 1.2 x
Two Balls Cost = 0.5 x
Two Balls Selling Price = 0.8(0.5)x
= 0.4 x
Profit = 2
Sales = cost + Profit
1.2 x + 0.4 x = x + 0.5 x + 2
1.6 x - 1.5 x = 2
0.1 x = 2
x = 20
Betty paid $20 for the bat and $5 for each ball.
yep. $20 bat and $10 for two balls. everyone repeat this so rajesh would have to write all our names.
plz tell me how u all come to that answer in detail, i am still getting tht the bat is 0.625 while each ball is 0.3125
just do rounding off.
Joe beat me to it. I made exactly the same equation.
The wording is a little misleading since it says "give away" the balls but actually they were sold at 80% of their value. Also it says "bats" when there was only one bat.
Bat = $20, Balls = $5 each
According to everyone if the bat cost 20, then the balls would cost 5. They are also stating that he made a profit of the balls which in reality he did not. Therefore, one should take into account that he is losing money on the balls:
x=bat cost
y=ball cost
x+2y=total cost
1.2x=total cost+2
1.2x=x+2y+2
.2x-2y=2
Assuming the bat cost $20, Then the balls should really cost $1. Which does not answer the question.
I'm with everyone else the bat's are $20.00 and the balls are $5.00 each
it's fairly simple math.
the sale was for bat=$24.00 (20x1.2)
balls =$8.00 ([5*2]*.8)
more thought on the way puzzle is written would help?
giving them away??
misleading
maybe i'm miss reading something...but i came up with
$10 bat
$5 balls each
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