Daniel and his children went into a bakery and where they sell cupcakes for $3.75 each and donuts for $1 each. daniel has $20 to spend and must buy a minimum of 7 cupcakes and donuts altogether. if xx represents the number of cupcakes purchased and yy represents the number of donuts purchased, write and solve a system of inequalities graphically and determine one possible solution.

The system of inequalities are x + y ≥ 7 and 3.75x + 1y ≤ 20 The one possible solution is 4 cupcakes and 3 donuts.

Solution:

Given, Daniel and his children went into a bakery and where they sell cupcakes for $3.75 each and donuts for $1 each.  

Daniel has $20 to spend and must buy a minimum of 7 cupcakes and donuts altogether.  

⇒ "x" represents the number of cupcakes purchased

⇒ "y" represents the number of donuts purchased,  

we have to write and solve a system of inequalities graphically and determine one possible solution.

Now, he should buy minimum 7 items, then x + y ≥ 7 ⇒ (1)

And, he has $20, so his maximum purchase is $20 then, 3.75x + 1y ≤ 20 ⇒ (2)

Now, suppose that he took 5 cupcakes, then he must take at least 2 donuts to satisfy (1)

So, substitute x and y values in (2)

⇒ 3.75(5) + 1(2) ≤ 20

⇒ 20.75 ≤ 20 ⇒ condition failed

So he can take maximum of 4 cupcakes only, and subsequently he has to take minimum of 3 donuts.

Hence, the one possible solution is 4 cupcakes and 3 donuts