the math team wraps gifts as a way to raise money for traveling to competitions. they offer two choices: a…

the math team wraps gifts as a way to raise money for traveling to competitions. they offer two choices: a plain wrapping or a decorative wrapping with bows. the table represents the money raised over a busy shopping weekend.\ngift - wrapping fundraiser\n|plain gifts wrapped|decorative gifts wrapped|total raised ($)|\n|----|----|----|\n|10|9|47|\n|25|12|86|\n|16|12|68|\nwhich statement describes the amounts the team charged for wrapping gifts?\nthe team charged $1 to wrap a gift with no bow and $2 to wrap a gift with a bow.\nthe team charged $2 to wrap a gift with no bow and $3 to wrap a gift with a bow.\nthe team charged $3 to wrap a gift with no bow and $4 to wrap a gift with a bow.\nthe team charged $4 to wrap a gift with no bow and $5 to wrap a gift with a bow.

the math team wraps gifts as a way to raise money for traveling to competitions. they offer two choices: a plain wrapping or a decorative wrapping with bows. the table represents the money raised over a busy shopping weekend.\ngift - wrapping fundraiser\n|plain gifts wrapped|decorative gifts wrapped|total raised ($)|\n|----|----|----|\n|10|9|47|\n|25|12|86|\n|16|12|68|\nwhich statement describes the amounts the team charged for wrapping gifts?\nthe team charged $1 to wrap a gift with no bow and $2 to wrap a gift with a bow.\nthe team charged $2 to wrap a gift with no bow and $3 to wrap a gift with a bow.\nthe team charged $3 to wrap a gift with no bow and $4 to wrap a gift with a bow.\nthe team charged $4 to wrap a gift with no bow and $5 to wrap a gift with a bow.

Answer

Explanation:

Step1: Definir variables

Sea $x$ el costo de envolver un regalo sin lazo y $y$ el costo de envolver un regalo con lazo.

Step2: Crear sistema de ecuaciones

A partir de la primera fila de la tabla: $10x + 9y=47$. A partir de la segunda fila: $25x+12y = 86$.

Step3: Multiplicar ecuaciones para eliminar una variable

Multiplicamos la primera ecuación por 4 y la segunda por - 3. Primera ecuación multiplicada: $40x + 36y=188$. Segunda ecuación multiplicada: $- 75x-36y=-258$.

Step4: Sumar ecuaciones

Sumando las dos ecuaciones obtenidas: $(40x - 75x)+(36y-36y)=188 - 258$. $-35x=-70$.

Step5: Resolver para $x$

Dividiendo ambos lados por - 35: $x = 2$.

Step6: Sustituir $x$ en una ecuación original

Sustituimos $x = 2$ en $10x + 9y=47$. $10\times2+9y=47$. $20 + 9y=47$. $9y=47 - 20$. $9y=27$. $y = 3$.

Answer:

El equipo cobró $2 para envolver un regalo sin lazo y $3 para envolver un regalo con lazo.