SOLUTION: I can’t find the answer... 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 $800$ pounds more than eac

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Question 1154226: I can’t find the answer...
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 $800$ 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?
Found 3 solutions by MathLover1, greenestamps, ikleyn:
Answer by MathLover1(20855) About Me  (Show Source):
You can put this solution on YOUR website!
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 800 pounds more than each of her trucks, but no more than %281%2F3%29 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%7B%7B%7B+truck+can+carry%2C+in+pounds%3F%0D%0A%0D%0Alet+a+large+truck+be+%7B%7B%7Bx and small trucks y
if your truck can carry a load of at least 800 pounds more than each of her trucks, we have
x=y%2B800........eq.1 ( = sign means assuming the greatest load you can be sure that my large truck can carry, in pounds)
if your truck can carry no more than %281%2F3%29 of the total load her four trucks, we have
x=%281%2F3%294y........eq.2
substitute x from eq.1
y%2B800=%281%2F3%294y
800=%281%2F3%294y-y
800=4y%2F3-3y%2F3

800=y%2F3
y=800%2A3
y=2400
go to
x=y%2B800........eq.1, substitute y
x=2400%2B800
x=3200->the greatest load you can be sure that my large truck can carry
so, your truck can carry 3200 pounds and each of her trucks can carry
2400

Answer by greenestamps(13367) About Me  (Show Source):
You can put this solution on YOUR website!


Let x be the number of pounds each of your neighbor's trucks can carry. Then the problem says

x%2B800+=+%281%2F3%29%2A4x
x%2B800+=+%284%2F3%29x%7D%7D%0D%0A%7B%7B%7B800+=+%281%2F3%29x
2400+=+x

Your neighbor's trucks can each carry 2400 pounds; yours can carry 2400+800 = 3200 pounds.

Answer by ikleyn(53937) About Me  (Show Source):
You can put this solution on YOUR website!
.
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 800 pounds more than each of her trucks,
but no more than 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?
~~~~~~~~~~~~~~~~~~~~~~~ 

The condition tells us these two facts

    M >= H + 800       (1)

    M <= %284%2F3%29H.        (2)

where M is "my" truck and H is "her" truck.


Or, in compound form

    H + 800 <= M <= %284%2F3%29H.


It implies

    H + 800 <= %284%2F3%29H.


Simplify by multiplying by 3 (both sides)

    3H + 2400 <= 4H

Hence,

    H >= 2400


Then from (1)

    M >= H + 800 = 2400 + 800 = 3200 pounds.    ANSWER


ANSWER.  3200 pounds is that greatest load "I" can be sure . . .

Solved.