Word problem:. Find the height of each building if Jefferson Square Tower is twice as tall as Lincoln Galleria and Washington Center is 120 feet taller than Lincoln Galleria. Total height 1800. Height each building?
Let x = height of Lincoln Galleria
Ley y = height of Jefferson Square Tower
Let z = height of Washington center
Since Jefferson Square Tower is twice as tall as Lincoln Galleria, we now know that
y = 2x
and Washington center is 120 feet taller than Lincoln, then
z = x + 120
The total height is 1800 feet, so that tells us x + y + z = 1800
Substitute the equations for y and z into the third equation (total height), and solve for x, then solve for y and z using that value.
1) If the total height is 1800, that means that all the heights add up to 1800. Since we don't know any of the heights, we need to give them variable names. We'll call Jefferson Square Tower x, Lincoln Galleria y, and Washington Center z. If we use these variable names with the statement that the total is 1800 we obtain the formula:
x + y + z = 1800
2) Since this formula has three variables, it is unsolvable. We need to get it down to one variable. To do this we will need the other information given in the problem. The problem says: "...Jefferson Square Tower is twice as tall as Lincoln Galleria..."
We can translate this to a formula by using our variable names and putting = where "is" was and 2* where "twice" is. Using this method, we obtain:
x = 2*y
Now we need to use the same method for "...Washington Center is 120 feet taller than Lincoln Galleria." (120 feet taller means 120 +) We get the formula:
z = 120 + y
3) Now we need to use substitution and simplify the original equation so we can solve it. Our two equations tell us that we can put 2*y wherever x is and 120 + y wherever z is. If we do this to our original formula (x + z + y = 1800), we get:
2*y + y + 120 + y = 1800
Now we can solve this because we only have one variable (y). Now let's add up all the like terms.
4*y + 120 = 1800
Now we solve for y by getting y on its own side with no numbers. We need to make sure we do the same thing to both sides.
4*y + 120 -120 = 1800 - 120 (subtract 120 from both sides)
(4*y)/4 = 1680/4 (divide both sides by 4)
y = 420
So the height of the Lincoln Galleria is 420ft.
4) Now use our formulas (x = 2*y and z = 120 + y) for each other building to find their heights. But now we know what y equals (420) so we can put that in instead of y.
x = 2*420 = 840
So the Jefferson Square Tower is 840ft tall.
z = 120 + 420 = 540
So the Washington Center is 540ft tall.
The first step of solving a story problem is labeling variables. For this problem, I will label the variables as:
x = Height of Jefferson Square Tower
y = Height of Lincoln Galleria
z = Height of Washington Center
Since we have three variables, we need to find at least three equations from the story problem.
The first sentence says that the Jefferson Square Tower (x) is (=) twice as tall (X 2) as the Lincoln Galleria (y). That produces the equation:
x = 2y
The second part of the sentence says that Washington Center (z) is (=) 120 feet taller (+120) than the Lincoln Galleria (y). That produces the equation:
z = 120 + y
The final statement is that the total height (x + y + z) is (=) 1800. That produces the equation:
x + y + z = 1800
Now that we have three equations, we can use substitution method to solve for our answers.
x + y + z = 1800 Equation 3
2y + y + z = 1800 Substitute the value of x in equation 1 into equation 3
3y + z = 1800 Simplify
3y + 120 + y = 1800 Substitute the value of z in equation 2 into the equatoin
4y + 120 = 1800 Simplify
4y + 120 - 120 = 1800 -120 Subtract 120 from each side
4y = 1680 Simplify
4y/4 = 1680/4 Divide each side by 4
y = 420 Simplify
x = 2y Equation 1
x = 2(420) Substitution
x = 840 Simplify
z = 120 + y Equation 2
z = 120 + 420 Substitution
z = 540 Simplify
Therefore, the height of Jefferson Square Tower is 840 feet, the height of Lincoln Galleria is 420 feet, and the height of Washington Center is 540 feet.