Question

Mia and her children went into a bakery that sells cupcakes for $2.50 each and donuts for $1.25 each. Mia has $30 to spend and must buy no less than 14 cupcakes and donuts altogether. If � x represents the number of cupcakes purchased and � y represents the number of donuts purchased, write and solve a system of inequalities graphically

Answer 1

2.50x + 1.25y ≤ 30

x + y ≥ 14

x ≤ 10 and y ≤ 24

Explanation:

we can by elimination if we multiply the second inequality by -2.5, we get:

-2.50x - 2.5y ≥ -35

if we add the first inequality to the above we get:

2.50x + 1.25y ≤ 30

+ -2.50x - 2.5y ≥ -35

-1.25y = -5

divide each side by -1.25 to get:

y = 4

therefore, x = 10

if you graph each system you must look for the area where the shading of each inequality overlaps

upon graphing, the solution is x ≥ 10 and y ≤ 24