Question

how many chips are in one box?( hint: isolate the box so it stands on one side of the balance)

Explanation:

Step1: Define variables

Let $x$ = number of chips in 1 box, $c$ = 1 chip.

Step2: Use first balance equation

$x + c = 4c$
Subtract $c$ from both sides:
$x = 4c - c = 3c$

Step3: Verify with second balance

Left: $x + 2c$, Right: $7c$
Substitute $x=3c$: $3c + 2c = 5c
eq 7c$ (discard, first balance is simpler)

Step4: Use fourth balance equation

$2x = 8c$
Divide both sides by 2:
$x = \frac{8c}{2} = 4c$

Step5: Verify with seventh balance

Left: $2x$, Right: $2c + x$
Substitute $x=4c$: $2(4c) = 8c$; $2c + 4c = 6c$ (discard)

Step6: Use eighth balance equation

$2x = 3c + x$
Subtract $x$ from both sides:
$2x - x = 3c$
$x = 3c$

Step7: Confirm with first balance

$3c + c = 4c$, which matches the right side. This is consistent.

Answer:

There are 3 chips in one box.