Question

The owner of a restaurant determines she can spend no more than $1600 to buy coffee for the next month. At wholesale prices, the regular coffee she uses costs $4.50 per pound and the decaffeinated coffee costs $6.00 per pound. The owner estimates she will need at least 60 pounds of coffee for the month. Which system of inequalities represents the possible combinations of the number of pounds of regular coffee, x, and the number of pounds of decaffeinated coffee, y, that meet these conditions? A 4.5x + 6y < 1600x + y > 60 B. 4.5x + 6y < 1600 x + y < 60 C. 4.5+ 6y < 60 x +y > 1600 D 4.5x + 6y > 1600 x + y > 60

Answer 1

A) 4.5x + 6y < 1600, x + y > 60

Step-by-step explanation:

Let the number of pounds of regular coffee = x

Let the number of pounds of decaffeinated coffee = y

Cost of regular coffee = $4.50 per pound

Cost of decaffeinated coffee = $6.00 per pound.

If she can spend no more than $1600 to buy coffee for the next month, then:

`4.50x+6.00y\le1600`

The owner estimates she will need at least 60 pounds of coffee for the month..

Therefore:

`x+y\ge60`

Therefore, the inequalities that meet these conditions are:

`\begin{gathered} 4.5x+6y<1600 \\ x+y>60 \end{gathered}`