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Dine de hiclo *-- ARIO PRE CLASE: Semana 1 0.06:47 restante Pdegina anterior Päcina siguiente Página 5 de 5 Pregunta 5 (1 punto) ✓ Guardado En una granja donde hay conejos y gallinas se contaron 132 cabezas y 420 patas. ¿Cuántos animales hay de cada especie? Selecclone 2 respuestas correctas 80 conejos 72 conejos 52 gallinas 78 conejos 60 gallinas 54 gallinas Plsina anterior Pägina sigulente Página 5 de 5

Dine de hiclo *--\newlineARIO PRE CLASE: Semana 11\newline00.0606:4747 restante\newlinePdegina anterior\newlinePäcina siguiente\newlinePágina 55 de 55\newlinePregunta 55 (11 punto) ✓ \checkmark Guardado\newlineEn una granja donde hay conejos y gallinas se contaron 132132 cabezas y 420420 patas. ¿Cuántos animales hay de cada especie?\newlineSelecclone 22 respuestas correctas\newline8080 conejos\newline7272 conejos\newline5252 gallinas\newline7878 conejos\newline6060 gallinas\newline5454 gallinas\newlinePlsina anterior\newlinePägina sigulente\newlinePágina 55 de 55

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Q. Dine de hiclo *--\newlineARIO PRE CLASE: Semana 11\newline00.0606:4747 restante\newlinePdegina anterior\newlinePäcina siguiente\newlinePágina 55 de 55\newlinePregunta 55 (11 punto) ✓ \checkmark Guardado\newlineEn una granja donde hay conejos y gallinas se contaron 132132 cabezas y 420420 patas. ¿Cuántos animales hay de cada especie?\newlineSelecclone 22 respuestas correctas\newline8080 conejos\newline7272 conejos\newline5252 gallinas\newline7878 conejos\newline6060 gallinas\newline5454 gallinas\newlinePlsina anterior\newlinePägina sigulente\newlinePágina 55 de 55
  1. Set up equations: Let's denote the number of rabbits as RR and the number of chickens as CC. We know that each rabbit has 44 legs and each chicken has 22 legs. We also know that the total number of heads (which is the same as the total number of animals) is 132132, and the total number of legs is 420420. We can set up the following system of equations:\newline11. R+C=132R + C = 132 (each animal has one head)\newline22. 4R+2C=4204R + 2C = 420 (each rabbit has 44 legs and each chicken has 22 legs)
  2. Solve for C: First, we'll solve the first equation for one of the variables. Let's solve for C:\newlineC=132−RC = 132 - R
  3. Substitute into second equation: Now, we'll substitute the expression for CC into the second equation: 4R+2(132−R)=4204R + 2(132 - R) = 420
  4. Distribute and simplify: Next, we'll distribute the 22 and simplify the equation: 4R+264−2R=4204R + 264 - 2R = 420
  5. Combine like terms: Combine like terms: 2R+264=4202R + 264 = 420
  6. Isolate term with R: Subtract 264264 from both sides to isolate the term with R:\newline2R=420−2642R = 420 - 264\newline2R=1562R = 156
  7. Solve for R: Divide both sides by 22 to solve for R:\newlineR=1562R = \frac{156}{2}\newlineR=78R = 78
  8. Find number of chickens: Now that we have the number of rabbits, we can find the number of chickens by substituting RR back into the equation for CC:
    C=132−RC = 132 - R
    C=132−78C = 132 - 78
    C=54C = 54

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