Andy had 20% fewer marbles than Henry. When Andy gave 80 marbles to Henry, the numbers of marbles he had left was half of what Henry had. How many marbles did Andy have in the begining?

Please help me

at start:

Henry ---- x marbles
Andy ---- .8x marbles

after give-away:
Henry --- x+80
Andy ---- .8x - 80

Andy's marbles = 1/2 of Henry's marbles

.8x-80 = (1/2)(x+80)
times 2
1.6x - 160 = x+80
.6x = 240
x = 400

So Henry had 400 and Andy had 320

check: after give-away
Andy is left with 240
Henry now has 480
Does Andy have half of what Henry has?? YES

To solve this problem, let's work through it step by step.

Let's assume that Henry had x marbles.

Since Andy had 20% fewer marbles than Henry, Andy would have 0.8x marbles.

When Andy gave 80 marbles to Henry, he would be left with 0.8x - 80 marbles.

We are told that the number of marbles Andy has left is half of what Henry has. So, we can set up the equation:

0.8x - 80 = 0.5x

Now, let's solve this equation to find the value of x, which represents the number of marbles Henry had initially.

0.8x - 0.5x = 80

0.3x = 80

Dividing both sides by 0.3:

x = 80 / 0.3

x ≈ 266.67

So, Henry initially had approximately 266.67 marbles.

Now, let's calculate how many marbles Andy had in the beginning. We know that Andy had 20% fewer marbles than Henry, so we can calculate Andy's initial number of marbles by subtracting 20% of x from x:

Andy's initial number of marbles = x - 0.2x

Andy's initial number of marbles = 0.8x

Substituting the value of x:

Andy's initial number of marbles ≈ 0.8 * 266.67

Andy's initial number of marbles ≈ 213.34

Therefore, Andy initially had approximately 213.34 marbles.

400for henry 320 for andy

at start:

Henry ---- x marbles
Andy ---- .8x marbles

after give-away:
Henry --- x+80
Andy ---- .8x - 80

Andy's marbles = 1/2 of Henry's marbles

.8x-80 = (1/2)(x+80)
times 2
1.6x - 160 = x+80
.6x = 240
x = 400

So Henry had 400 and Andy had 320

check: after give-away
Andy is left with 240
Henry now has 480
Does Andy have half of what Henry has?? YES