Sanju and manju went to a bakery shop.?

sanju and manju went to a bakery shop. sanju ate 4 puffs, 3 burgers, 2 cakes, and used up all the money she had. manju ate 3 puffs,6 burgers,and 4 cakes and paid 25% more than that sanju paid . what % of sanju's money was spent on the puffs she ate? give me method and solve it please.......Sanju and manju went to a bakery shop.?
S - money Sanju spent

M - money Manju spent

p, b, c - prices of puffs, burgers and cakes, respective.



three equations

S = 4p + 3b + 2c ...(1)

M = 3p + 6b + 4c ... (2)

M = 1.25 S ... (3)



First, we'll eliminate M equalizing right sides of (2) and (3)

1.25 S = 3p + 6b + 4c ...(4)

when we compare this to (1) we can notice members containing b and c are scaled by factor two; we're gonna use this to eliminate both b and c.

Divide (4) by 2 to get

0.625 S = 1.5 p + 3b + 2c

move 1.5p to the left side so that group (3b+2c) stays alone on the right

0.625 S - 1.5 p = 3b + 2c ...(5)

Do the same with (1) to get:

S - 4p = 3b + 2c ...(6)

From (5) and (6)

0.625 S - 1.5 p = S - 4p

0.375 S = 2.5 p

p = 0.375 S / 2.5 = 0.15 S

This means price of one puff is 15% of money Sanju spent.

She bought 4 puffs so money she spent on puffs is 4*15=60% of all the money she had.

The answer is 60%



Note:

Instead of dividing (4) by 2, we could multiply (1) by 2 to get

2S = 8p + 6b + 4c

and then from this equation and (4):

2 S - 8p = 1.25 S - 3p

0.75 S = 5 p

price of one puff is

p = 0.75 S / 5 = 0.15 S

and price of 4 puffs is 0.6 S

- the same result as before.Sanju and manju went to a bakery shop.?
Let S be the money Sanju spent

M be the money Manju spent

p, b, c be the prices of puffs, burgers and cakes, respectively.



three equations that an be formed

S = 4p + 3b + 2c .....................(A)

M = 3p + 6b + 4c ... .................(B)

M = 1.25 S ............................ (C)



Multiply (A) by 2

2 S = 8p + 6b + 4c...................(D)

Deduct (B) from (D)

2S - M = 8p - 3p

2S - 1.25S = 5p

0.75S = 5p

0.15 S = p

But Sanju ate 4 puffs

4p = 0.15S x 4 = 0.6 S = 60% of S

So Sanju has spent 60 % of his money for the puffs