Question

the triangular region shows the number of possible raisins, x, and number of possible chocolate chips, y, a baker can use in a recipe. which combination of raisins and chocolate chips can the baker use? 45 raisins and 10 chocolate chips 33 raisins and 25 chocolate chips 28 raisins and 20 chocolate chips 55 raisins and 12 chocolate chips

Explanation:

Step1: Define boundary line equations

First, find the equation of the top line: passes through (0,40) and (60,10). Slope $m=\frac{10-40}{60-0}=-\frac{1}{2}$. Equation: $y=-\frac{1}{2}x+40$.
Bottom line: passes through (0,0) and (60,15). Slope $m=\frac{15-0}{60-0}=\frac{1}{4}$. Equation: $y=\frac{1}{4}x$.
Also, $x\geq25$ from the left boundary of the shaded region.

Step2: Test Option 1 (45,10)

Check if $10\geq\frac{1}{4}(45)=11.25$? No, fails bottom line.

Step3: Test Option 2 (33,25)

Check if $25\leq-\frac{1}{2}(33)+40=23.5$? No, fails top line.

Step4: Test Option 3 (28,20)

Check $x\geq25$: $28\geq25$ ✔️
Check $20\geq\frac{1}{4}(28)=7$ ✔️
Check $20\leq-\frac{1}{2}(28)+40=26$ ✔️
All conditions satisfied.

Step5: Test Option 4 (55,12)

Check if $12\leq-\frac{1}{2}(55)+40=12.5$ ✔️, but $12\geq\frac{1}{4}(55)=13.75$? No, fails bottom line.

Answer:

28 raisins and 20 chocolate chips