Question

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?

Answer 1

The correct statements will be,

1. Lemonade cans and water bottles' summation will be less than or equal to 360.
2. Another situation can be that value of lemonade cans are 1.5 times the value of water bottles.
3. At least 142 water bottles must be sold to cover the costs associated with renting the costumes.

The calculations done above can be represented in a form of equations by using the applications of simple algebraic expressions, which is shown in the part below.

Calculation of bottles and cans.

• We can express the situation as in (1) by using the equation below,

• $\rm No.\ of\ Water\ Bottles + No.\ of\ Lemonade\ Cans\leq 360\ units \\\\OR\\\\WB+LC\leq 360\ units$

• The situation given as under (2) can also be expressed as,

• $\rm Water\ Bottles= \ 500- 1.5(Lemonade\ Cans)$

• A situation as under (3) can be calculated by extracting the given values and finding the number of bottles that needs to be sold to receive $500 so as the costs of renting the costumes is achieved.

• $\rm (144\ x\ \ 2)+ (WB x \ 1.5)= 500\\\\\\WB =\dfrac{ \ 500-\ 288 }{1.5}$

• Calculating further,

• $\rm WB = \dfrac{212}{1.5}\\\\\rm WB = 144.33$

• It is certain that the one-third units of a water bottle cannot be sold, and hence the drama club will have to sell 142 units of water bottle to recover its costs of renting costumes.

Hence, the algebraic expressions are already expressed above, and it can be determined that a total of 142 units of water bottles must be sold to recover the costs of renting costumes.

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