Question

stuff to make you think
13 based on this mobile, determine if these equations are true or false.
key: ❤️ = h 🌙 = m ★ = s
a h + s + s + h = m + m + h
b 2s + h = 2m
c 6h + 6s = 6m + 3h
d 2m + h = h + 2s + h
e 3s + 2h = 2m + h + s
f 3h = 2m + 2s

Explanation:

Step1: Analyze the mobile balance

Since the mobile is balanced, the total weight on the left - hand side is equal to the total weight on the right - hand side. From the mobile, we have $3h + 2s=2m + h$, which simplifies to $2h+2s = 2m$ or $h + s=m$.

Step2: Check equation (a)

Given $h + s + s+h=m + m+h$. Substitute $m = h + s$ into the right - hand side: $m + m+h=(h + s)+(h + s)+h=3h + 2s$. The left - hand side is $2h + 2s$. Since $3h + 2s
eq2h + 2s$, this equation is false.

Step3: Check equation (b)

Given $2s+h = 2m$. Since $m=h + s$, then $2m=2(h + s)=2h + 2s$. Since $2s+h
eq2h + 2s$, this equation is false.

Step4: Check equation (c)

Given $6h + 6s=6m+3h$. Substitute $m = h + s$ into the right - hand side: $6m+3h=6(h + s)+3h=6h+6s + 3h=9h + 6s$. Since $6h + 6s
eq9h + 6s$, this equation is false.

Step5: Check equation (d)

Given $2m+h=h + 2s+h$. Substitute $m = h + s$ into the left - hand side: $2m+h=2(h + s)+h=2h+2s + h=3h + 2s$. The right - hand side is $2h + 2s$. Since $3h + 2s
eq2h + 2s$, this equation is false.

Step6: Check equation (e)

Given $3s + 2h=2m+h + s$. Substitute $m = h + s$ into the right - hand side: $2m+h + s=2(h + s)+h + s=2h+2s+h + s=3h + 3s$. Since $3s + 2h
eq3h + 3s$, this equation is false.

Step7: Check equation (f)

Given $3h=2m+2s$. Substitute $m = h + s$ into the right - hand side: $2m+2s=2(h + s)+2s=2h+2s+2s=2h + 4s$. Since $3h
eq2h + 4s$, this equation is false.

Answer:

(a) False
(b) False
(c) False
(d) False
(e) False
(f) False