|
Question 6720: 1. The first side of a triangle is 2 feet longer than the second. The third side is triple the second. The perimeter of the triangle is 42 feet. Find the length of each side of the triangle.
Define the variable expressions.
Write an equation.
Solve the equation and determine the values asked for.
2. Anna is a store supervisor. The sales clerk earns $4000 per year less than Anna. The sum of Anna's annual salary and the clerk's annual salary is $61,200. Find Anna's and the clerk's annual salaries.
Define the variable expressions.
Write an equation.
Solve the equation and determine the values asked for.
Help
Found 3 solutions by prince_abubu, artemis911, longjonsilver:
Answer by prince_abubu(198)   (Show Source):
You can put this solution on YOUR website! Let's do the triangle problem first.
The first side of the triangle (let's call it F) is longer than the second (let's call it S) by 2 feet, right? Translating that into an equation would bring you to  .
CAUTION!!! It's very tempting to translate the sentence to  , thinking that just because F is longer, it receives the +2. The S is shorter, so it needs the +2 to be as long as F.
The third side (let's call it T) is triple the second. Again, it's tempting to say 3T = S. It's really  . The T is larger than the S, as implied, so it doesn't need the tripling.
OK. The perimeter is the sum of the sides, so  in this case. We're going to have to substitute the F and the T so that the perimeter equation is only going to be in 1 variable instead of 3. Since and , we can rewrite the perimeter equation as:
 <---- we combined like terms.
 <----- subtracted 2 from both sides.
 <----- We see that the length of the second side turned out to be 8 feet. If the first side is 2 feet longer than the second, then the first side is 10 feet. If the third side is triple the second side, then the third side is 3*8 = 24 feet. Add up all the sides and you should get 42 feet total. So, 8 + 10 + 24 = 42 feet.
---------------------------------------------------------
Let A be what Anna earns. The problem does say that the clerk earns less than she does, by $4000. The equation, then for what the clerk earns is  .
WARNING: Just because the sentence was written about the clerk's salary with the variables and constant amounts in that order, it doesn't mean that the order will be the same in the written equation. It's so tempting to just write  or  <---- the mistaken equations.
Anna obviously earns more than the clerk. That makes first mistaken equation wrong, because Anna's yearly salary is obviously more than $4000 if the problem said that she earned $4000 more than the clerk. The second mistaken equation is wrong because it implies that the clerk earned more money than Anna. If Anna earned more, then you would definitely have to subtract $4000 from her earnings to total the salary of the clerk. So the correct equation for the clerk's salary is  .
So, their total earnings for the year was $61,200. So,  .
We'll need to substitute A - 4000 for the C so that the equation will only be in one variable. We then have:
 <----combined like terms
 <--- add 4000 to both sides
 <---- So Anna earned $32,600. If the clerk earned $4000 less, then the clerk must've earned $28,600.
Answer by artemis911(3) (Show Source):
Answer by longjonsilver(2297)  (Show Source):
You can put this solution on YOUR website! the artemis solution is badly wrong. Ignore it.
Let middle length be x --> side2
so, side1 is x+2
and side3 is 3x
perimeter is 3 sides added to give 42, so
x + x+2 + 3x = 42
5x + 2 = 42
5x = 40
x = 8
so, three sides are 8, 10 and 24
jon.
|
|
|
| |
