Question

I own a large truck, and my neighbor owns four small trucks that are all identical. My truck can carry a load of at least $600$ pounds more than each of her trucks, but no more than $\frac{1}{3}$ of the total load her four trucks combined can carry. Based on these facts, what is the greatest load I can be sure that my large truck can carry, in pounds?

Answer 1

Answer:

  there is no greatest load

Step-by-step explanation:

Let x and y represent the load capacities of my truck and my neighbor's truck, respectively. We are given two relations:

  x ≥ y +600 . . . . . my truck can carry at least 600 pounds more

  x ≤ (1/3)(4y) . . . . . my truck carries no more than all 4 of hers

Combining these two inequalities, we have ...

  4/3y ≥ x ≥ y +600

  1/3y ≥ 600 . . . . . . . subtract y

  y ≥ 1800 . . . . . . . . multiply by 3

My truck's capacity is greater than 1800 +600 = 2400 pounds. This is a lower limit. The question asks for an upper limit. The given conditions do not place any upper limit on truck capacity.

Answer 2

Answer:

$\large \boxed{\text{2400 lb}}$

Step-by-step explanation:

We have two condition:

    Let x = the load of your truck

   and y = load of their trucks Then

(1)       x ≥ y + 600  

       4y = the total load of their four trucks

⅓ × 4y = the load  of load of your truck

(2)  ⁴/₃x ≤ y

Calculations:  

$\begin{array}{lrcll}(1) & x & = & y+ 600\\(2)& x & =&\dfrac{4}{3}y\\\\(3)& x - 600 & =&y&\text{Subtracted 600 from each side of (1)}\\& x & = & \dfrac{4}{3}(x - 600)&\text{Substituted (3) into (2)}\\\\&3x & = & 4(x - 600)&\text{Multiplied each side by 3}\\\end{array}$

$\begin{array}{lrcll}&3x & = & 4x - 2400&\text{Distributed the 4}\\&3x + 2400 & = & 4x&\text{Added 2400 to each side}\\ & x & = & \mathbf{2400}&\text{Subtracted 3x from each side}\\\end{array}\\\text{The greatest load my truck can carry is \large \boxed{\textbf{2400 lb}} }}$