Question

write an equation that represents this hanger diagram. then solve for n. first, write an equation that represents this hanger diagram. (the diagram shows a hanger with two sides: one side has a purple rectangle labeled 24 and two green circles labeled n; the other side has a purple rectangle labeled 6 and five green circles labeled n.)

Explanation:

Step1: Analyze the hanger diagram

The top side has a block of 24 and 2 \(n\)s, so its total is \(24 + 2n\). The bottom side has a block of 6 and 5 \(n\)s, so its total is \(6 + 5n\). Since the hanger is balanced, these two totals are equal. So the equation is \(24 + 2n = 6 + 5n\).

Step2: Solve the equation for \(n\)

Subtract \(2n\) from both sides: \(24 = 6 + 3n\). Then subtract 6 from both sides: \(18 = 3n\). Divide both sides by 3: \(n = 6\).

Answer:

The equation is \(24 + 2n = 6 + 5n\) and \(n = 6\).