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

there is no greatest load

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

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

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 & =&(4)/(3)y\\\\(3)& x - 600 & =&y&\text{Subtracted 600 from each side of (1)}\\& x & = & (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 $\large \boxed{\textbf{2400 lb}}$}}`