Question

Alex, Bryan and Charles had a total of 284 marbles. The number of marbles Bryan had was 1/2 the number of marbles Charles had. After Alex and Bryan each gave away 1/2 of their marbles, the 3 boys had 166 marbles left. How many marbles did Alex have at first?

Answer 1

Alex had 236 marbles at first.

Explanation:

Let's assume the number of marbles Charles had as C.

According to the given information, Bryan had half the number of marbles Charles had, so Bryan had C/2 marbles.

Alex, Bryan, and Charles had a total of 284 marbles, so we can write the equation: Alex + Bryan + Charles = 284.

After Alex and Bryan each gave away half of their marbles, they had 166 marbles left. This means they gave away half of their original number of marbles, so we can write the equation: (Alex/2) + (Bryan/2) + Charles = 166.

Now, let's solve these equations to find the values.

From the first equation, we can rewrite it as Alex + C/2 + C = 284.

From the second equation, we can rewrite it as (Alex/2) + (C/4) + C = 166.

Combining the terms, we get:

Alex + C/2 + C = 284

(Alex/2) + (C/4) + C = 166

To simplify the equations, let's multiply the second equation by 2:

Alex + C/2 + C = 284

Alex + C/2 + 2C = 332

Subtracting the first equation from the second equation:

2C - C/2 = 332 - 284

(4C - C)/2 = 48

3C/2 = 48

3C = 96

C = 96/3

C = 32

Now that we have the value of C, we can substitute it back into the first equation to find Alex's value:

Alex + 32/2 + 32 = 284

Alex + 16 + 32 = 284

Alex + 48 = 284

Alex = 284 - 48

Alex = 236

Therefore, Alex had 236 marbles at first.

Answer 2

Let, initially Alex, Bryan and Charles have x, y and z marbles respectively.

Then x + y + z = 284 ……(1)

y = 1/2z ……(2)

(x - x/2) + (y - y/2) + z = 166

x + y + 2z = 332 ……(3)

Subtract equation (1) from equation (3)

z = 332 - 284

z = 48

y = 1/2z = 1/2 * 48 = 24

Substitute y = 24 and z = 48 in equation (1).

x + 24 + 48 = 284

x = 284 - y - z

= 284 - 24 - 48

= 284 - 72

= 212

Alex have 212 marbles at first.