Math Help - Word Problems

1. Word Problems

Please help me with these word problems! All i need is the equation, I will be able to solve the rest but I just cannot get the equations!

1. In an office building, a room contains 54 chairs. The number of chairs per row is three less than twice the number of rows. Find the number of rows and the number of chairs per row.

2. The area of a triangle is 51 square inches. One side of the triangle is one inch less than three times the length of the altitude to that side. Find the length of that side and the length of the altitude to that side.

2. Originally Posted by christina.brooks
Please help me with these word problems! All i need is the equation, I will be able to solve the rest but I just cannot get the equations!

1. In an office building, a room contains 54 chairs. The number of chairs per row is three less than twice the number of rows. Find the number of rows and the number of chairs per row. ...
Let r denote the number of rows and n the number of chairs per row.

From the wording of the question you know:

n = 2r -3 and

n * r = 54

Solve this system of equations. (For confirmation only: I've got 6 rows)

3. Originally Posted by christina.brooks
...

2. The area of a triangle is 51 square inches. One side of the triangle is one inch less than three times the length of the altitude to that side. Find the length of that side and the length of the altitude to that side.
The area of a triangle is calculated by:

$a = \frac12 \cdot s \cdot h$

Let s denote the length of the side and h the length of the height then you know:

s = 3h - 1

Plug in this term into the equation of the area and you'll get:

$a = \frac12 \cdot (3h -1) \cdot h$

Plug in the value for a and solve for h

(For confirmation only: I've got h = 6)