Bonny baked some cookies. She gave 2/5 of them and an additional 15 cookies to a neighbor. 4/5 of the remainder and an additional 10 cookies to her sister. If she was left with 40 cookies, how many cookies did she bake ?
starting with x cookies,
2/5 given, leaving 3/5 x
15 more, leaving 3/5 x - 15
4/9 of that, leaving 5/9 (3/5 x - 15)
10 more, leaving 5/9 (3/5 x - 15) - 10
so, now you know that
5/9 (3/5 x - 15) - 10 = 40
or
(x-55)/3 = 40
x = 175
It’s actually
Bonny baked some cookies. She gave 2/5 of them and an additional 15 cookies to a neighbor. 4/9 of the remainder and an additional 10 cookies to her sister. If she was left with 40 cookies, how many cookies did she bake ?
Yes I did. Oobleck is correct
To find out how many cookies Bonny initially baked, we need to work backward from the information provided in the question.
Let's break down the information given step by step:
1) Bonny gave away 2/5 of the cookies to her neighbor, along with an additional 15 cookies. So the fraction of cookies she gave away can be represented as 2/5n, where 'n' represents the total number of cookies.
2) After giving away 2/5 of the cookies and the additional 15 cookies, she was left with a certain number of cookies. Let's call the remaining number of cookies 'x'. So, the equation becomes x = (3/5)n - 15.
3) Then, Bonny gave away 4/5 of the remaining cookies (which is 'x') to her sister, along with an additional 10 cookies. This can be represented as 4/5x + 10.
4) After giving away 4/5 of the remaining cookies and the additional 10 cookies, she was left with 40 cookies. So, the equation becomes 40 = (1/5)x - 10.
Now, let's solve these equations to find the value of 'n', which represents the number of cookies Bonny initially baked.
From equation 3, we have x = (3/5)n - 15.
Substituting the value of x in equation 4, we have 40 = (1/5)((3/5)n - 15) - 10.
Simplifying further, we get 40 = (3/25)n - 3 - 10.
Combining like terms, we get 40 = (3/25)n - 13.
To get rid of the fraction, we can multiply both sides of the equation by 25, giving us 1000 = 3n - 325.
Bringing '3n' to the left-hand side and simplifying, we have 3n = 1325.
Dividing both sides by 3, we get n = 1325/3 ≈ 441.67.
Since cookies cannot be divided into decimals, Bonny must have initially baked the nearest whole number of cookies, which is 442 cookies.
gave (2c / 5 + 15) to neighbor
remainder = c - 2c/5 - 15 = 3c/5 -15
gave sister (4/5)(3c/5 -15) + 10 = 12 c/25 - 12 + 10 = (12c - 50)/25
left with
c - (2c / 5 + 15) - (12c - 50)/25 = 40
25c/25 - 10c/25 - 375/25 -12c/25 + 50/25 = 40
3 c -325 = 25*40 = 1000
3 c = 1325
c = 442
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