Question

1. dominic has an unknown number of quarters in a bag. he knows that when he places them on a scale and adds six more quarters to the same side, it will balance with 15 quarters on the right side.

(a) let ( n ) be the number of coins in the bag. write an equation that you can solve for ( n ) and solve it below.
(b) show the same process by crossing (subtracting) out the same number of coins from both sides of the scale

Explanation:

Step1: Define equation for balance

$n + 6 = 15$

Step2: Isolate $n$ via subtraction

$n + 6 - 6 = 15 - 6$

Step3: Simplify to find $n$

$n = 9$

Step4: Subtract 6 coins from both sides

On the left side: Remove the 6 extra quarters, leaving only the bag with $n$ coins.
On the right side: Remove 6 of the 15 quarters, leaving $15 - 6 = 9$ quarters.
The scale remains balanced, so $n = 9$.

Answer:

(a) The solved value is $n = 9$
(b) After crossing out 6 coins from both sides, the left side has the bag with $n$ coins, and the right side has 9 coins, confirming $n = 9$.