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: 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

$P-0=\dfrac{16-0}{0-16}(W-16)\\\\\Rightarrow W+P=16.$

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

$P-0=\dfrac{15-0}{0-20}(W-20)\\\\\Rightarrow 3P+4W=60.$

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.

Answer 2

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

Step-by-step 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.