Question

Tom is going to turn little Quacker into roast duck! He goes to the grocery store to get some salt and pepper seasoning to his duck dinner. Salt costs .50 cents per scoop. Pepper cost .75 cents per scoop, and he wants to speand less that $5. He plans to bring home no more than 8 scoops of seasoning

Answer 1

He can buy 3 scoops of salts and 4 scoops of pepper or 4 scoops of salts and 3 scoops of pepper spent maximum.

Explanation:

Given that:

The cost of salt = 50 cents / scoop =$ 0.5 / scoop

The cost of pepper =75 cents / scoop = $ 0.75 / scoop

Let he buys x scoops of salt and y scoops of pepper.

As he plans to bring home no more than 8 scoops of seasoning, so

`x+y\leq8\cdots(i)`

The total cost of x scoops of salt and y scoops of pepper = 0.5x+0.75y

As he wants to spend less than $5, so

`0.5x+0.75y<5 \\\\ \Rightarrow 50x+75y<500 \\\\\Rightarrow 2x+3y <20\cdots(ii)`

Here,
`x\geq 0, y \geq 0` and x,y are counting numbers.

On plotting the graph of equations (ii) and (ii), the possible solution is the integral values in the shaded as shown in the figure.

The maximum possible integral values, for expances less than $5, are (x,y)=(3,4), (4,3).

Hence, he can buy 3 scoops of salts and 4 scoops of pepper or 4 scoops of salts and 3 scoops of pepper to spent maximum.