Question

To raise money to attend Boy Scout camp Alec is selling popcorn.?small bags of popcorn sell for $4 each and large bag sale for $6 each. he needs to earn at least $300 to attend camp you also earn a badge if he sells 60 bags total of any combination. write a system of linear inequalities to represent this situation

Answer 1

Let small bags of popcorn be represented by = x

Let large bags be represented by = y

Price of small bag = $4

Price of large bag = $6

A minimum of $300 is required to attend the camp so

`4x+6y\leq300` .............(1)

Also given is that a badge is earned if Alec sells 60 bags

So, equation is

`x+y=60` ............(2)

Answer 2

The system of linear inequalities to represent the situation :

x+y = 60

4x+6y≥300

Explanation:

We are given that :

Cost of one small popcorn bag is $4

Cost of one large popcorn bag $6

Let no. of small popcorn bags Alec sold be x

Let no. of large popcorn bags Alec sold be y

Cost of x small popcorn bag is $4x

Cost of y large popcorn bag $6y

Since she sold total 60 bags .

So, equation becomes:

x+y = 60 --(a)

Since she had to earn at least $300.

So, equation becomes:

4x+6y≥300 --(b)

Thus the system of linear inequalities to represent the situation :

x+y = 60

4x+6y≥300