# 3X3 system word problem

• Feb 12th 2008, 11:08 AM
Itsbaxagain
3X3 system word problem
A certain 18-hole golf course has par-3, par-4 and par-5 holes and there are twice as many par-4 holes as there are par-5 holes. How many holes of each type are there if a golfer has par on every hole for a score of 70?

All I need is the 3 equations to solve it and I'll be able to do the rest.
• Feb 12th 2008, 11:57 AM
Soroban
Hello, Itsbaxagain!

Quote:

A certain 18-hole golf course has par-3, par-4 and par-5 holes.
There are twice as many par-4 holes as there are par-5 holes.
How many holes of each type are there if a golfer has par on every hole for a score of 70?

Let: . $\displaystyle \begin{Bmatrix}x &=&\text{no. of par-3 holes} \\ y &=&\text{no. of par-4 holes} \\ z &=&\text{no. of part-5 holes} \end{Bmatrix}$

There are 18 holes on the course: .$\displaystyle {\color{blue}x + y + z \:=\:18}$

There are twice as many $\displaystyle y's$ as $\displaystyle z's\!: \;\;y \:=\:2z\quad\Rightarrow\quad {\color{blue}y - 2x \:=\:0}$

A golfer made par on every hole for a score of 70: .$\displaystyle {\color{blue}3x + 4y + 5z \:=\:70}$

. . . Go for it!