Question

Brooke and Samuel had the same number of marbles. Brooke gave away 20 marbles and Samuel gave away 44 marbles. Brooke then had 3 times as many marbles as Samuel. How many marbles did Brooke and Samuel each have at first?

Answer 1

Brooke and Samuel each initially had 56 marbles. By setting up an algebraic equation to represent the given conditions, we solve to find the number of marbles they started with.

Step-by-step explanation:

The student asks how many marbles Brooke and Samuel each had at first, given that Brooke gave away 20 marbles and Samuel gave away 44 marbles, and afterwards, Brooke had three times as many marbles as Samuel. Let's denote the initial number of marbles they each had as 'x'. After Brooke gave away 20 marbles, she had 'x - 20' marbles left. Samuel, having given away 44 marbles, had 'x - 44' marbles. The condition given is that Brooke then had three times as many marbles as Samuel, which translates into the equation:

x - 20 = 3(x - 44)

Solving this equation, we get:

x - 20 = 3x - 132

2x = 112

x = 56

So, Brooke and Samuel each initially had 56 marbles. The subject involves basic algebra, commonly taught in middle school mathematics.

Answer 2

Given:

Brooke and Samuel had same number of marbles.

Let x and y be the number of marbles Brooke and Samuel had.

At first, x=y ... (1)

(x-20)=3(y-44) .... (2)

Substitute equation (1) in (2,

`y-20=3(y-44)`
`y-20=3y-132`
`3y-y=132-20`
`2y=112`
`y=56`

Therefore, Brooke and Samuel each have 56 marbles each at first.