information about the costs of three party plans at jubilee bowling and arcade is shown in the…

information about the costs of three party plans at jubilee bowling and arcade is shown in the table.\njubilee bowling and arcades party plans\nplan a: $12 per person plus a flat $30 service fee\nplan b: $15 per person plus a flat $20 service fee\nplan c: $18 per person with no service fee\ndevante can spend no more than $140 on his birthday party at jubilee bowling and arcade. what is the greatest number of people, including himself, that devante can have at his birthday party without spending more than $140?\na 7\nb 8\nc 9\nd 10

information about the costs of three party plans at jubilee bowling and arcade is shown in the table.\njubilee bowling and arcades party plans\nplan a: $12 per person plus a flat $30 service fee\nplan b: $15 per person plus a flat $20 service fee\nplan c: $18 per person with no service fee\ndevante can spend no more than $140 on his birthday party at jubilee bowling and arcade. what is the greatest number of people, including himself, that devante can have at his birthday party without spending more than $140?\na 7\nb 8\nc 9\nd 10

Answer

Explanation:

Step1: Escribir la ecuación para Plan A

Sea $n$ el número de personas. El costo del Plan A es $C_A = 12n+30$.

Step2: Resolver la desigualdad para Plan A

Queremos $C_A\leq140$, es decir $12n + 30\leq140$. Restamos 30 de ambos lados: $12n\leq140 - 30=110$. Luego $n\leq\frac{110}{12}\approx9.17$.

Step3: Escribir la ecuación para Plan B

El costo del Plan B es $C_B=15n + 20$.

Step4: Resolver la desigualdad para Plan B

Queremos $C_B\leq140$, es decir $15n+20\leq140$. Restamos 20 de ambos lados: $15n\leq140 - 20 = 120$. Luego $n\leq\frac{120}{15}=8$.

Step5: Escribir la ecuación para Plan C

El costo del Plan C es $C_C = 18n$.

Step6: Resolver la desigualdad para Plan C

Queremos $C_C\leq140$, es decir $18n\leq140$. Luego $n\leq\frac{140}{18}\approx7.78$.

Answer:

B. 8