Algebra Questions I'm struggling with ?

First question is: The total curb weight of a truck, a car A, and a car B is 11450 lb. The weight of car A is 5 lb less than two B cars. The truck weighs 2155 more than car A. What is the curb weight of each vehicles?

Second question is: Find k so the the line containing the points (-3,k) and (4,12) is parallel to the line containing the points (5,4) and (1,-5)

These are the only two I'm struggling with :( I'd appreciate the help. 

Update:

Thank you so much for the help on the first question! Really clears up what I was doing wrong. 

But I still need some help on the second question please!

2 Answers

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  • 4 weeks ago

    call them T,A,B

    T + A + B = 11450

    A = 2B – 5

    T = 2155 + A

    T + A + B = 11450

    (2155 + A) + A + B = 11450

    B = (A + 5)/2

    (2155 + A) + A +  (A + 5)/2 = 11450

    2155 + 2A + (A + 5)/2 = 11450

    2A + (A + 5)/2 = 9295

    4A + A + 5 = 18590

    5A = 18585

    A = 3717

    B = (A + 5)/2

    B = (3717 + 5)/2 = 1861

    T = 2155 + A

    T = 2155 + 3717 = 5872

    check

    T + A + B = 11450

    5872 + 3717 + 1861 = 11450 ok

    A = 2B – 5

    3717 = 2•1861 – 5 = 3717 ok

    T = 2155 + A

    5872 = 2155 + 3717 ok

  • 4 weeks ago

    This is a system of three equations and three unknowns:

    Let t = weight of the truck

    Let a = weight of car A

    Let b = weight of car B

    You are told the total weight is 11,450 lb, so:

    a + b + t = 11450

    Then the weight of car A is 5 lb less than two B cars:

    a = 2b - 5

    And finally, the truck weighs 2,155 lb more than car A:

    t = a + 2155

    We have "a" in terms of "b" and "t" in terms of "a".  So let's start with taking the second equation and substituting that expression into equations 1 and 3:

    a + b + t = 11450 and t = a + 2155

    2b - 5 + b + t = 11450 and t = 2b - 5 + 2155

    simplify and now we have a system of two equations and two unknowns:

    3b - 5 + t = 11450 and t = 2b + 21503b + t = 11455 and t = 2b + 2150

    We have t in terms of b, so substitute that into the first equation and solve for b:

    3b + t = 11455

    3b + 2b + 2150 = 11455

    5b = 9305

    b = 1861

    Now that we have b, we can solve for a, then use that to solve for t:

    a = 2b - 5

    a = 2(1861) - 5

    a = 3722 - 5

    a = 3717

    t = a + 2155

    t = 3717 + 2155

    t = 5872

    The weight of the three vehicles are:

    The truck is 5,872 lb, car A is 3,717 lb, and car B is 1,861 lb.

    • Anonymous4 weeks agoReport

      Thank you soooo much! This is incredibly helpful. 

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