Question

Ezra and Tara sold at least 150 coupon books.Ezra sold at most 30 books more than twice the number Tavares sold. Show and describe all possible combinations of the numbers of coupon books Ezra and Tavares sold.List Teo possible combinations.

Answer 1

Ezra and Tara sold at least 150 coupon books. Ezra sold at most 30 books more than twice the number Tavares sold. There are two possible combinations: (150, 0) and (151, 70).

Step-by-step explanation:

Let's start by setting up some equations to represent the given information. Let E represent the number of coupon books Ezra sold and T represent the number of coupon books Tavares sold.

We know that Ezra and Tavares sold at least 150 coupon books, so we have the equation: E + T ≥ 150.

We also know that Ezra sold at most 30 books more than twice the number Tavares sold, so we have the inequality: E ≤ 2T + 30.

To find all the possible combinations, we can test different values for T and solve for E.

Let's start with T = 60. Plugging this value into the inequality, we have: E ≤ 2(60) + 30, which simplifies to E ≤ 150. Since E + T must be greater than or equal to 150, the only possible combination is E = 150 and T = 0.

Now let's try T = 70. Plugging this value into the inequality, we have: E ≤ 2(70) + 30, which simplifies to E ≤ 170. Since E + T must be greater than or equal to 150, the possible combinations are E = 150 and T = 0, or E = 151 and T = 70.

So, the two possible combinations are: (150, 0) and (151, 70).

Answer 2

Answer: The answers are (110,40), (120,45), (130,50), etc.

Step-by-step explanation: Given that Ezra and Tara sold at least 150 coupon books and Ezra sold at most 30 books more than twice the number Tavares sold. We are to list the possible combinations of the numbers of coupon books Ezra and Tavares sold.

Let, 'x' and 'y' be the number of coupon books sold by Ezra and Tavares respectively. Then according to the question, we have

`x+y\geq 150\\\\x-30\leq 2y.`

Writing these inequalities as equations, we have

`x+y=150,\\\\x-30=2y~~\Rightarrow x-2y=30.`

Multiplying the first equation by 2 and adding to the second equation, we have

`2x+x=300+30\\\\\Rightarrow 3x=330\\\\\Rightarrow x=110.`

So,

`y=150-110=40.`

Thus, the possible combinations are

(110,40), (120,45), (130,50),etc.