Question

happy groundhog day!
groundhog day, celebrated in the united states and canada on february 2nd, is a quirky and beloved tradition where the emergence of a groundhog from its burrow is observed to predict whether there will be six more weeks of winter or an early spring, based on whether or not the groundhog sees its shadow.
directions: use your math skills to find the value of each icon and the ? in the puzzle below.
three groundhog icons with plus signs between them = 564
one groundhog icon + two tree icons with multiplication sign between them = 384
one flower - butterfly icon - one tree icon = 93
two top - hat icons with multiplication sign between them = one flower - butterfly icon - 26
one groundhog icon + one flower - butterfly icon - one tree icon × one top - hat icon =?
2529
169

Explanation:

Step1: Calcular valor de la marmota

Sean $G$ la marmota con sombrero. $3G = 564$, así que $G = \frac{564}{3} = 188$

Step2: Calcular valor del bosque

Sean $F$ el bosque. $G + F^2 = 384$. Sustituimos $G$: $188 + F^2 = 384$, entonces $F^2 = 384 - 188 = 196$, así que $F = \sqrt{196} = 14$

Step3: Calcular valor del grupo de flores

Sean $B$ el grupo de flores. $B - F = 93$. Sustituimos $F$: $B = 93 + 14 = 107$

Step4: Calcular valor del sombrero

Sean $H$ el sombrero. $H^2 = B - 26$. Sustituimos $B$: $H^2 = 107 - 26 = 81$, así que $H = \sqrt{81} = 9$

Step5: Calcular el valor final

Aplicamos orden de operaciones: $G + B - F \times H = 188 + 107 - (14 \times 9)$
Primero la multiplicación: $14 \times 9 = 126$
Luego sumas y restas: $188 + 107 = 295$; $295 - 126 = 169$

Answer:

169