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