"Jeremy, Sue, And Holly Are Siblings. Sue Was Born Three Years Before Holly, And Jeremy Was Born Five Years Before Sue. The Product Of Sues Age And Je

Jeremy, Sue, and Holly are siblings. Sue was born three years before Holly, and Jeremy was born five years before Sue. The product of Sues age and Jeremys age is at most 150. If x represents the age of Holly, which inequality can be used to find the age of each sibling?

A. x2 + 8x + 15 ≤ 150

B. x2 - 11x + 24 ≤ 150

C. x2 + 8x ≤ 150

D. x2 + 11x + 24 ≤ 150

 

Answer:

D. x^2 + 11x + 24 ≤ 150

Step-by-step explanation:

Step 1: Let x be the age of Holly

Step 2: Sue was born three years before Holly.

This means that Sue was 3 yrs older than Holy.

If x is the age of Holly,

then Sue is 3 yrs older than Holly, then Sues age should be x+3

Step 3: Jeremy was born five years before Sue.

Meaning Jeremy was 5 yrs older than Sue.

If Sues age is x+3, and Jeremy was 5 yrs older than Sue, then Jeremys age should be x+3+5. To simplify further, x+8.

Step 4:

Lets see the information we gathered:

x = Hollys age

x+3 = Sues age

x+8 = Jeremys age

Step 5: The product of Sues age and Jeremys age is at most 150.

Then:

(x+3)(x+8) ≤ 150

Simplify:

(x)(x)+(3x+8x)+(3)(8) ≤ 150

x^2 + 11x + 24 ≤ 150

Final answer:

x^2 + 11x + 24 ≤ 150