Jonathan is in charge of ordering the trophies. There are three types, which cost $17, $32, and $49.

Question

Identify the variables.

Write the system of equations for the following problem.

Solve

 

Full Question didnt fit in question.

Jonathan is in charge of ordering the trophies for a school awards banquet. There are three types, which cost $17, $32, and $49. He needs to order some of each for a total of 35 trophies and a total cost of $1285. He needs 8 fewer of the $17 trophies than of the $32 trophies. How many $49 trophies does he need to order?

Answer 1

Let x be the number of $17 trophies.

Let y be the number of $32 trophies.

Let z be the number of $49 trophies.

 

There are a total of 35 trophies:

x + y + z = 35

 

The total cost is $1285

17x + 32y + 49z = 1285

 

He needs 8 fewer of the $17 trophies than of the $32 trophies

x = y - 8

 

These three equations are your system. You can use the third and substitute into the first two to eliminate x and simplify:

 

(y-8) + y + z = 35

17(y-8) + 32y + 49z = 1285

 

From here, combine like terms and simplify. You now have two equations with two unknowns, and can solve relatively easily using either the substitution or elimination methods. I'll leave that up to you.

 

If you have further questions, please comment.