The ratio of the number of cheesecakes to the number of mango cakes was 3:2. After Baker Lam sold 144 cheesecakes, the ratio became 3:5.

A) How many cheesecakes did Baker Lam bake at first?
B)Baker Lam decided to deliver the remaining cakes to 4 charity homes. How many cakes did each home receive?

To solve this problem, we can use a method called proportion. Let's break down the information given step by step.

A) How many cheesecakes did Baker Lam bake at first?

1. Let's represent the number of cheesecakes as 3x and the number of mango cakes as 2x. This means that the ratio of cheesecakes to mango cakes is 3:2.

2. After Baker Lam sold 144 cheesecakes, the new ratio became 3:5. This indicates that there are now 3 parts of cheesecakes to 5 parts of mango cakes.

3. We know that Baker Lam sold 144 cheesecakes, which represents 3 parts of our initial ratio. Therefore, we can write the equation: (3x)/(3) = 144.

4. Solving this equation, we can find the value of x. Dividing both sides by 3, we get: x = 144.

5. Now that we have the value of x, we can find the initial number of cheesecakes by substituting x back into our previously defined representation. So, initial number of cheesecakes = 3x = 3 * 144.

Therefore, Baker Lam initially baked 432 cheesecakes.

B) Baker Lam decided to deliver the remaining cakes to 4 charity homes. How many cakes did each home receive?

1. To find out how many cakes each home will receive, we need to determine the total number of remaining cakes.

2. Since we know that the new ratio is 3:5 and Baker Lam sold 144 cheesecakes, we can subtract 144 from the total number of cheesecakes.

3. The initial number of cheesecakes was 432, and we subtracted 144, so the remaining cheesecakes are 432 - 144 = 288.

4. Now, we can divide the remaining cheesecakes equally among the 4 charity homes. To find out how many cakes each home will receive, we need to divide 288 by 4.

Therefore, each charity home will receive 72 cakes.

A) Well, it seems like Baker Lam was really cheesed off! So, let's assume the initial number of cheesecakes was 3x and the number of mango cakes was 2x. After selling 144 cheesecakes, we're left with 3x - 144 cheesecakes. According to the new ratio, this is equal to 3/5 of the total number of cakes, which is 5x.

So, we can set up the equation: 3x - 144 = (3/5)(5x)
If we solve this equation, we get x = 80.
And if x = 80, then the initial number of cheesecakes was 3x = 3(80) = 240.
So, Baker Lam baked 240 cheesecakes at first.

B) Now, let's divide the remaining cakes among the 4 charity homes. We have 240 cheesecakes left and the same amount of mango cakes as before. So, each home would receive 240/4 = 60 cheesecakes.
Looks like the charity homes are in for some cheesy goodness!

A) To find out how many cheesecakes Baker Lam baked at first, let's assume the number of cheesecakes is 3x, where x is a common factor.

According to the given information, the ratio of cheesecakes to mango cakes was 3:2 initially.
So, the number of mango cakes is 2x.

After Baker Lam sold 144 cheesecakes, the ratio became 3:5.
Now, the number of cheesecakes is 3x - 144, and the number of mango cakes is 5x.

Therefore, we can set up the equation:
(3x - 144) / (2x) = 3 / 5.

Cross-multiplying, we get:
5(3x - 144) = 3(2x).

Simplifying the equation, we have:
15x - 720 = 6x.

Bringing the like terms to one side:
15x - 6x = 720,
9x = 720.

Now, divide both sides by 9 to find the value of x:
x = 720 / 9,
x = 80.

So, the number of cheesecakes Baker Lam baked at first is 3x = 3 * 80 = 240 cheesecakes.

B) Baker Lam decides to deliver the remaining cakes to 4 charity homes.
The remaining number of cakes is the total number of cakes minus the sold number of cheesecakes, which is 240 - 144 = 96 cakes.

To find out how many cakes each home receives, divide the remaining cakes by the number of homes:
96 cakes / 4 homes = 24 cakes.

Therefore, each charity home receives 24 cakes.

if there were c cheesecakes and m mangocakes,

c/m = 3/2
(c-144)/m = 3/5

c = 240
m = 160

check:
240/160 = 3/2
96/160 = 3/5

after the sales, there were 96+160 = 256 cakes

divide that by 4 to get the number for each home.

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