Betty and Charlie shared a packet of sweets. Betty would have 48 more sweets more than Charlie if Charlie gave 2/5 of his sweets to Betty. If Charlie gave 5/8 of his sweets to Betty, he would have 192 less sweets than Betty. How many sweets did Betty have?

Question

Betty and Charlie shared a packet of sweets. Betty would have 48 more sweets more than Charlie if Charlie gave 2/5 of his sweets to Betty. If Charlie gave 5/8 of his sweets to Betty, he would have 192 less sweets than Betty. How many sweets did Betty have?

Answer 1

Let's assume that Betty initially had B sweets, and Charlie had C sweets.

If Charlie gave 2/5 of his sweets to Betty, Betty would get 2/5*C = (2/5)*C = (2/5)*C sweets
And since Charlie gave Betty 48 sweets, we have 2C/5 = 48
Multiplying both sides of the equation by 5/2 gives us 5C/2 = 48
Multiplying both sides by 2/5, C = 48 * 2/5 = 19.2

This means Charlie initially had 19.2 sweets, which is impossible since the number of sweets cannot be in decimal values. Therefore, our assumption is wrong.

Now let's assume Charlie initially had c sweets, where c is a whole number.

If Charlie gave 5/8 of his sweets to Betty, Betty would get 5/8*c = (5/8)*c = (5/8)*c sweets
And since Charlie gave Betty 192 sweets, we have 5c/8 = 192
Multiplying both sides of the equation by 8/5 gives us 8c/5 = 192
Multiplying both sides by 5/8, c = 192 * 5/8 = 120

This means Charlie initially had 120 sweets.

So, if Charlie gave 5/8 of his sweets, Betty would get 5/8*120 = 75 sweets
In this case, Betty would have 75 + 192 = <<75+192=267>>267 sweets. Answer: \boxed{267}.

Answer 2

Let's assume that Charlie initially had x sweets.

According to the first condition, if Charlie gives 2/5 of his sweets to Betty, Betty would have 48 more sweets than Charlie. This can be represented as:

Betty's sweets = Charlie's sweets + 48
(Betty's sweets = x + 48)

Now, if Charlie gives 5/8 of his sweets to Betty, he would have 192 fewer sweets than Betty. This can be represented as:

Charlie's sweets = Betty's sweets - 192
Charlie's sweets = (x + 48) - 192
Charlie's sweets = x - 144

We can equate the two expressions for Charlie's sweets:

x - 144 = x + 48

By subtracting x from both sides, we get:

-144 = 48

This is not possible, so there must have been a mistake in the question.

Could you please recheck the information given?

Answer 3

To solve this problem, let's start by assigning variables to the unknown quantities.

Let's assume the number of sweets that Charlie initially has is C, and the number of sweets that Betty initially has is B.

According to the first condition of the problem, if Charlie gives 2/5 of his sweets to Betty, Betty will have 48 more sweets than Charlie.

So, we can write the following equation:
B = C + 48 ----(Equation 1)

Now, let's consider the second condition. If Charlie gives 5/8 of his sweets to Betty, he would have 192 fewer sweets than Betty.

So, we can write the following equation:
C = B - 192 ----(Equation 2)

Now, we can solve this system of equations to find the values of B and C.

Substituting Equation 2 into Equation 1, we get:
B = (B - 192) + 48

Simplifying this equation:
B = B - 192 + 48
B = B - 144

Bringing B terms together:
B - B = -144
0 = -144

This equation has no solution, which means there is no value of B that satisfies both conditions given in the problem. Therefore, there is no unique answer to this problem, and we cannot determine the number of sweets Betty had.