Hi Bob,
There are three vehicles involved--a truck and two cars, designated A and B. We are given their total curb weight, which is defined as the weight of the vehicles with a full tank and all consumables (oil, antifreeze, etc.) necessary for operation, but not including any passengers...here total curb weight is 11, 450 lb. . If we let "t" stand for the curb weight of the truck alone, and "a" and "b" stand for the curb weight of cars A and B, respectively, we have:
1) t + a + b = 11, 450 lb.
We are also told that the weight of car A "...is 15 lb. less than the weight of two B cars." This can be represented in symbols by:
2) a = 2b - 15 lb.
Finally, we have one more piece of given information--the truck weighs 2155 lb. more than car A, or, in symbols:
3) t = a + 2155 lb.
So we have three equations in three unknowns. Our goal will be to use equations two and three, which give us equivalents for a in terms of b, and t in terms of a, to rewrite equation one using only the substitutions which produce a one-variable equation we can solve for b. Then we will plug b's value into equation two, solving for a; plugging a's value into equation three will give the final curb weight for t.
3) t = a + 2155 lb. AND
2) a = 2b - 15 lb. .
Substitute 2) into 3) to get (leaving aside the lb. symbol for convenience):
4) t = [ 2b - 15] + 2155 .
Now put both 2) and 4) into equation 1),
making t + a + b = 11, 450 lb.
into { [ 2b - 15] + 2155 } + {2b - 15} + b = 11, 450 lb.
This looks like a mess (!)...BUT we have eliminated all other variables except "b," and so when we have combined like terms on the left side we get
5) 5b + 2125 = 11, 450 lb. .
Subtracting 2125 from both sides and dividing by 5 yields
6) b = 1865 lb. . This is the weight of car B.
Plugging this value back into equation 2 gives us
7) a = 2 (1865 lb. ) - 15 = 3715 lb. , the curb weight of car A.
Finally, plugging this value for a back into equation 3) gives
8) t = ( 3715 lb. ) + 2155 lb. = 5870 lb. , the curb weight of the truck.
For a check, car B has curb weight 1865 lb. , car A 3715 lb. , and the truck 5870 lb. . These three curb weights, when added, total 11, 450 lb. .
Hope this helps.
David Foster
