Fiona baked some cookies. 4/5 of the cookies baked were chocolate cookies and the rest were coconut cookies. After giving away 75% of the chocolate cookies and 1/2 of the coconut cookies, there were 96 cookies left. How many cookies did Fiona bake?

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checking the bot's answer:

if she had 160 cookies, then 128 were chocolate and 32 were coconut

she gave away 3/4 of the 128 or she gave away 96 chocolates, leaving
her with 32 chocolates cookies.
she gave away 1/2 of the cocos, leaving her with 16 coconuts
leaving her with a total of 32+16 or 48 cookies, but it said 96

THE BOT IS WRONG AGAIN.

correct solution:
at start:
chocolates: 4/5 x
cocos : 1/5 x

the give-away:
chocs left = (1/4)(4x/5) = x/5
cocos left = (1/2)(1/5 x) = x/10

x/5 + x/10 = 96
times 10
2x + x = 960
x = 320 <----- number she baked
so there were 4/5 of 320 or 253 chocolate and
1/5 of 320 or 64 coconut cookies.

To solve this problem step-by-step, let's break it down into smaller parts:

Step 1: Determine the number of cookies Fiona baked initially.
Let's assume that Fiona initially baked a total of x cookies.

Step 2: Calculate the number of chocolate cookies.
Given that 4/5 of the cookies baked were chocolate cookies, we can write the equation:
Number of chocolate cookies = (4/5) * x

Step 3: Calculate the number of coconut cookies.
The remaining cookies after giving away some of them were coconut cookies, so we can write the equation:
Number of coconut cookies = x - Number of chocolate cookies

Step 4: Calculate the number of chocolate cookies after giving away.
Fiona gave away 75% of the chocolate cookies, which means she kept 25% of them. Hence, we can write the equation:
Number of chocolate cookies after giving away = (25/100) * Number of chocolate cookies

Step 5: Calculate the number of coconut cookies after giving away.
Fiona gave away 1/2 of the coconut cookies, so the number of coconut cookies remaining is:
Number of coconut cookies after giving away = (1/2) * Number of coconut cookies

Step 6: Calculate the total number of cookies remaining.
The total number of cookies remaining is the sum of the chocolate cookies after giving away and the coconut cookies after giving away, which can be written as:
Total number of cookies remaining = Number of chocolate cookies after giving away + Number of coconut cookies after giving away

Step 7: Set up the equation.
Given that there were 96 cookies left, we can write the equation:
Total number of cookies remaining = 96

Step 8: Solve the equation.
Now we can plug in the known values into the equation and solve for x:
96 = (25/100) * Number of chocolate cookies + (1/2) * Number of coconut cookies

Step 9: Solve for x.
Simplifying the equation, we get:
96 = (25/100) * (4/5) * x + (1/2) * (1/5) * x

Multiplying the fractions:
96 = (1/4) * x + (1/10) * x

Adding the fractions:
96 = (10/40) * x + (4/40) * x
96 = (14/40) * x

To get rid of the fraction, we multiply both sides of the equation by 40:
96 * 40 = 14 * x
3840 = 14x

Dividing both sides by 14, we find:
3840/14 = x
x ≈ 274.286

Since we are dealing with whole numbers and cookies cannot be divided into decimals, we round the number of cookies Fiona initially baked to the nearest whole number.

Therefore, Fiona baked approximately 274 cookies.

To solve this problem, let's break it down step by step.

Step 1: Find the number of chocolate cookies Fiona baked.
- Since 4/5 of the cookies were chocolate cookies, we can calculate the number of chocolate cookies by multiplying the total number of cookies by 4/5.
- Let's represent the total number of cookies as "x" and the number of chocolate cookies as "4x/5".

Step 2: Find the number of coconut cookies Fiona baked.
- The rest of the cookies, after subtracting the chocolate cookies, are coconut cookies. Therefore, the number of coconut cookies baked is x - 4x/5.

Step 3: Calculate the number of chocolate cookies remaining after giving away 75%.
- 75% of the chocolate cookies were given away, so the number of chocolate cookies remaining is 25% of 4x/5.
- This can be calculated as (25/100) * (4x/5) = 1/4 * 4x/5 = x/5.

Step 4: Calculate the number of coconut cookies remaining after giving away 1/2.
- 1/2 of the coconut cookies were given away, so the number of coconut cookies remaining is 1/2 of (x - 4x/5).
- This can be calculated as (1/2) * (x - 4x/5) = 1/2 * (5x/5 - 4x/5) = 1/2 * (x/5) = x/10.

Step 5: Calculate the total number of cookies remaining.
- The total number of cookies remaining is the sum of the chocolate cookies remaining and the coconut cookies remaining: x/5 + x/10.

Step 6: Set up and solve the equation.
- According to the problem, there were 96 cookies left, so we can set up the equation: x/5 + x/10 = 96.

To solve this equation, we need to find a common denominator, which is 10 in this case.

Multiply the first term by 2/2 and the second term by 1/1, we get:
2x/10 + x/10 = 96.

Combine the terms:
(2x + x)/10 = 96.

Simplify:
3x/10 = 96.

Multiply both sides by 10:
3x = 960.

Divide both sides by 3 to isolate x:
x = 320.

Step 7: Find the total number of cookies baked.
- The total number of cookies baked is represented by "x", which we have just found to be 320.

Therefore, Fiona baked a total of 320 cookies.

Fiona baked 160 cookies.