Nicole R. answered • 01/01/14

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Dynamic Emory Goizueta Graduate Tutoring Multiple Subjects

Hey Laura,

There's actually a second way to do the problem that introduces systems of equations:

- First, you write an equation for the number of seats. Say that "x" is the number of seats that sit 2 children and "y" is the number of seats that sit 3 children. You know that x + y = 7.
- Furthermore, you know that 2 students sit in each "x" seat and 3 in each "y" seat, and the total must be 19 children, so you can say 2x + 3y = 19.
- Now you have two equations: x + y = 7 and 2x + 3y = 19.
- Isolate one variable, let's say x, from x + y = 7 by subtracting y from both sides and getting x = 7-y. Now substitute that into the second equation.
- So 2x + 3y = 19, and x = 7 - y. So you have 2(7-y) + 3y = 19.
- Multiply that out to get 14 - 2 y + 3y = 21. Simplify by adding like terms to get 14 + y = 19. Then subtract 14 from both sides, so y = 5.
- Then plug the y =5 into the first equation, x + y = 7. You have x + 5 = 7. Subtract 5 from both sides to get x = 2.

Hope that helps as another way to think about the problem!