Question

Can someone answer these 2 questions and tell me how you solved it?

1. Five hundred tickets were sold for a certain music concert. The tickets for the adults and children sold for $7.50 and $4.00, respectively, and the total receipts for the performance were $3,312.50. How many of each kind of ticket were sold.

2. A warehouse operator has up to 20,000 square feet of floor space in which to store two products. Each unit of product X requires 10 square feet of floor space and costs $15 per day to store. Each unit of product Y requires 40 square feet of floor space and costs $10 per day to store. The total storage cost per day cannot exceed $17,000. Write a system of Linear inequalities that describes the various ways the two products can be stored.​

Answer 1

1. 375 adult tickets and 125 children's tickets

2. 10x +40y ≤ 20,000; 15x +10y ≤ 17,000

Explanation:

1.

For problems involving mixtures or combinations of two kinds of objects, it is often convenient to choose a variable to represent the object contributing the most to the mix. Here, the adult tickets contribute more to revenue than children's tickets, so we'll use "a" to represent the number of adult tickets sold. Then the number of children's tickets sold is (500-a), since the total is 500 tickets.

The revenue from ticket sales is said to be ...

7.50a + 4.00(500-a) = 3312.50

3.50a +2000 = 3312.50 . . . . eliminate parentheses, collect terms

3.50a = 1312.50 . . . . . . . . . . . subtract 2000

1312.50/3.50 = a = 375 . . . . . divide by the coefficient of "a"

Then the number of children's tickets sold is

(500-a) = 500-375 = 125

375 adult tickets and 125 children's tickets were sold.

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2.

You are given two relationships that must be met. One inequality can be written for each one.

Up to 20,000 ft² of space is available

10x + 40y ≤ 20,000 . . . . . total the area taken by each product

Storage cost per day cannot exceed $17,000

15x + 10y ≤ 17,000 . . . . . . total the storage costs for each product