Question

Tennis balls are sold in packages of 3. Golf balls are sold in packages of 12. A sporting goods store orders 15 packages of balls. The total number of balls is 126.
The system of linear equations g plus t equals fifteen, Twelve g plus three t equals one hundred and twenty-six represents the scenario where g is the number of packages of golf balls and t is the number of packages of tennis balls.
The system of linear equations is graphed below.
How many packages of tennis balls were ordered?

6 packages

9 packages

12 packages

15 packages

Answer 1

In a way, the problem already explains what you have to do. You bought fifteen cases of balls, either golf or tennis. So the equation of the number of cases you have is :
g + t = 15

Likewise, you know the number of balls you have: 126. The 126 balls are either golf or tennis balls, coming from the number of balls per case. Since you know that there are 12 golf balls in a golf case and 3 tennis balls in a tennis case, you know that:

12*the number of golf ball cases (or g) + 3*the number of tennis ball cases (or t) = 126; 12g + 3t = 126.

The problem actually gave you all you need to solve this. To solve any equation, you just need like terms, or only one of a variable. 12g +3t= 126 has two variables, so we can change that. Looking back at g +t = 15, solve for either g or t. (in my case, I'll solve for g). So g = 15-t.

Now we know that g is equivalent to 15-t. Looking at the 12g + 3t =126, plug in 15-t for g. Now you get:

12(15-t) +3t =126.

This way, you'll be able to solve for t. To solve for g, just plug in the value of t in g = 15-t.