Question

A supermarket employee is making a mixture of cashews and almonds. Cashews cost $7 per pound, and almonds cost $5 per pound. The employee wants to make less than 6 pounds of the mixture and wants the total cost of the nuts used in the mixture to be not more than $30. Let x represent the number of pounds of cashews. Let y represent the number of pounds of almonds. Select all inequalities that represent constraints for this situation.
A. x + y ≤ 6

B. 7x + 5y < 6

C. x + y < 6

D. 7x + 5y > 30

E. 7x + 5y ≤ 30

F. x + y ≤ 30

Answer 1

Because he needs less than (note that he didn't say he needs no more than) 6 pounds, first inequality is C) x+y<6

Now in inequalities that have 7 and 5 in them, 7 represents the cost of first ingredient and 5 the cost of second ingredient. If we multiply each of that number with quantity of that ingredient and sum both up we get the price of the mixture.

Because he says that he wants that mixture costs no more than 30 that means that it costs less than 30 but 30 can be the answer as well.

The last answer is E)  7x + 5y $\leq 30$