Question

A baker prepared 264 more cookies than muffins. She sold 3/8 of the cookies and half of the muffins. She had 588 cookies and muffins left altogether. How many cookies did she bake at first?​

Answer 1

She baked 640 cookies at first.

Explanation:

Let cookies be x and muffins be y,

Let cookies remaining be z and remaining muffins be a

x = 264 + y

now,

x - 3/8 of x = z

x - 3x/8 = z

or, (8x-3x)/8 = z

so, z = 5x/8

Now,

y - y/2 = a

or, (2y-y)/2 = a

so, a = y/2

Now,

z + a = 588

or, 5x/8 + y/2 = 588

as we know x = 264 + y,

or, 5(264 + y)/8 + y/2 = 588

or, (1320 + 5y)/ 8 + y/2 = 588

or, (2640 + 10y + 8y)/16 = 588

or, 2640 + 18y = 9408

or, 18y = 9408 - 2640

or, 18y = 6768

so, y = 6768/18

so, y = 376

now,

x = 264 + y

or, x = 264 + 376

so, x = 640