Mitul is buying snacks for the student council meeting. She wants to buy 400 cookies. Cookies are available at a store in two different sizes of packages: small (S) and large (L). There are only 6 large packages left at the store and Mitul can spend a maximum of $60 on cookies. The table below shows the number of cookies and the cost of the two package sizes.Which system of inequalities represents this situation?24S + 36L ≥ 4003S + 5L ≥ 60L ≤ 6 24S + 36L ≤ 4003S + 5L ≤ 60L ≤ 6 24S + 36L ≥ 4003S + 5L ≤ 60L ≤ 6 24S + 36L ≤ 4003S + 5L ≥ 60L ≥ 6
Question
Mitul is buying snacks for the student council meeting. She wants to buy 400 cookies. Cookies are available at a store in two different sizes of packages: small (S) and large (L). There are only 6 large packages left at the store and Mitul can spend a maximum of $60 on cookies. The table below shows the number of cookies and the cost of the two package sizes.Which system of inequalities represents this situation?24S + 36L ≥ 4003S + 5L ≥ 60L ≤ 6 24S + 36L ≤ 4003S + 5L ≤ 60L ≤ 6 24S + 36L ≥ 4003S + 5L ≤ 60L ≤ 6 24S + 36L ≤ 4003S + 5L ≥ 60L ≥ 6
Solution
Para resolver este problema, debemos formular un sistema de desigualdades que represente las restricciones dadas. Vamos a analizar cada una de las condiciones:
- Mitul quiere comprar al menos 400 galletas.
- Solo hay 6 paquetes grandes disponibles en la tienda.
- Mitul puede gastar un máximo de $60 en galletas.
Primero, definamos las variables:
- representa el número de paquetes pequeños.
- representa el número de paquetes grandes.
De acuerdo con la tabla:
- Cada paquete pequeño contiene 24 galletas y cuesta $3.
- Cada paquete grande contiene 36 galletas y cuesta $5.
Ahora, formulamos las desigualdades:
-
La cantidad total de galletas debe ser al menos 400:
-
El costo total no debe exceder $60:
-
Solo hay 6 paquetes grandes disponibles:
Por lo tanto, el sistema de desigualdades que representa esta situación es:
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