Answer:
B. [tex]x^2+11x+24\leq 150[/tex]
Step-by-step explanation:
Step 1) Defining Sue and Jeremy's ages using x
Sue is 3 years older than Holly (h):
[tex]h=x+3[/tex]
Jeremy is 5 years older than Sue, or 8 years older than Holly (j):
[tex]j=x+8[/tex]
Product of Jeremy and Sue's ages is less than or equal to 150:
[tex]hj\leq 150[/tex]
Step 2) Simplifying into a single equation
Using the equation above we can substitute Sue and Jeremy's ages:
[tex](x+3)(x+8)\leq 150[/tex]
Now we can simplify this equation. Use the distributive property first:
[tex]x(x+8)=x^2+8x\\3(x+8)=3x+24[/tex]
Now add all the terms together and get the final answer:
[tex]x^2+8x+3x+24\leq 150\\x^2+11x+24\leq 150[/tex]
Final equation: [tex]x^2+11x+24\leq 150[/tex]
