Question

Boris wants to buy pineapples and watermelons, He wants to buy a total of at least 16 fruits (condition A) with $60 at most (condition B) The graph represents the constraints on the number of pineapples P and watermelons W Boris buys.

Boris buys 6 pineapples. How many watermelons can he buy to meet both his constraints?

Answer 1

Answer: There must be atleast 10 watermelons that he can buy.

Explanation:

Since we have given that

Number of pineapples bought by Boris = 6

Let the number of watermelons bought by Boris be 'x'.

According to question, it is given that he wants to buy a total of atleast 16 fruits.

So, our equation becomes,

`6+x\geq 16`

We need to find the number of watermelons that he can buy.

`6+x\geq 16\\\\x\geq 16-6\\\\x\geq 10`

Hence, there must be atleast 10 watermelons that he can buy.

Answer 2

Answer: The answer is 10 watermelons.

Step-by-step explanation: Given that Boris is going to buy pineapples and watermelons, a total of at least 16 fruits with $60 at most. The graph in the question represents the constraints on the number of pineapples P and watermelons W Boris buys.

From the graph, we have for condition A:

Two points are (16,0) and (0,16). So, the first constraint in equation form will be

`P-0=(16-0)/(0-16)(W-16)\\\\\Rightarrow W+P=16.`

And the constraint will be

`P+W\geq 16.`

Also, from the graph, we have for condition B:

Two points are (20,0) and (0,15). So, the second constraint in equation form will be

`P-0=(15-0)/(0-20)(W-20)\\\\\Rightarrow 3P+4W=60.`

And the constraint will be

`3P+4W\leq 60.`

If Boris buy 6 pineapples, then from conditions A and B, we have

`W\geq 10~~\textup{and}~~W\leq 10.5.`

These will give us that W = 10.

Thus, Boris can buy 10 Watermelons to meet both his constraints.