35 The drama club is running a lemonade stand to raise money for its new production. A local grocery store donate cans of lemonade and bottles of water. Cans of lemonade sell for $2 each and bottles of water sell for $1.50 each. The club needs to raise at least $500 to cover the cost of renting costumes. The students can accept a maximum of 360 cans and bottles. Write a system of inequalities that can be used to represent this situation. The club sells 144 cans of lemonade. What is the least number of bottles of water that must be sold to cover the cost of renting costumes?

a. c+b≤360 ... equation 1

b. 2 c+1.5 b≥500 ... equation 2, where c and b are the number of cans and bottles of water respectively.

c. The number of water bottles to be sold have to be equal to or more than 142 to cover the cost of renting costumes.

Explanation:

a.

Step 1: Determine maximum number of cans and bottles

As indicated, the number of cans and bottles can not exceed a certain value. This means that the number of cans and bottles can be either equal to or less than that value. The maximum number of cans and bottles can be represented in the following expression;

c+b≤m

where;

c=unknown

b=unknown

m=360

replacing;

c+b≤360 ... equation 1

b.

Step 2: Determine total amount needed to raise $500

Since $500 dollars is the minimum amount needed, the sales have to be $500 and more. This can be expressed as;

(C*c) + (B*b) ≥T

where;

T=total amount needed

C=price per can of lemonade

c=number of cans sold

B=price per bottle of water

b=number of bottles sold

In our case;

T=$500

C=$2

c=unknown

B=$1.50

b=unknown

replacing;

(2*c) + (1.5*b) ≥500

2 c+1.5 b≥500 ... equation 2

c.

Step 3: Determine least number of bottles of water that must be sold

The least number of bottles of water that must be sold to cover the cost of renting costumes can be solved using equation 2 above;

2 c+1.5 b≥500

where;

c=144

b=unknown

replacing;

(2*144) + 1.5 b≥500

288+1.5 b≥500

1.5 b≥500-288

1.5 b≥212

b≥212/1.5=141.33=142

b≥142, meaning the number of water bottles to be sold have to be equal or more than 142 to cover the cost of renting costumes.