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The substitute is in!. x=algebra. By: Drake Hudspeth 03/07/11 Math-03. The Problem.

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the substitute is in

The substitute is in!

x=algebra

By: Drake Hudspeth

03/07/11

Math-03

the problem
The Problem
  • The school that Stefan goes to is selling tickets to a choral performance. On the first day of ticket sales the school sold three senior citizen tickets and one child ticket for a total of 38$. The school took in 52$ on the second day by selling three senior citizen tickets and two child tickets. Find the price of a senior citizen ticket and the price of a child ticket.

Equations-

3x+y=38

3x+2y=52

graphing
Graphing
  • Use Microsoft Excel.
  • Plot your point in cells B2 and C2-B8 and C8.
  • Use cell A1 to put x.
  • In A2-A8 put -5,-3,-1,0,1,3,and5.
  • Put your equation in cells B1 and C1.
  • Go to insert and choose graphs.
  • Pick the x and y graph.

The reason that I do not recommend this system is because there is no way to go back and see why you missed the answer and because you must first solve for y.

substitution
Substitution
  • Start with one equation. 3x+y=38
  • Subtract the x on both sides. 3x-3x+y=38-3x
  • You now use this y on the next equation. 3x+2(38-3x)=52
  • Distribute or multiply what is outside of the parenthesis with what is inside of it. 3x+76-6x=52
  • Combine like terms. -3x=-24
  • Divide the two terms that you have. X=8
  • Use x to solve for y. 3(8)+y=38
  • Distribute. 24+y=38
  • Subtract the integer on the left from the integer on the right.

38-24=14

  • You now have y. y=14
  • So x=8 and y=14.

I enjoy this method because it is accurate and there are many steps to see where you have made a mistake.

elimination
Elimination
  • You must use both equations in the beginning. First subtract one integer from the other. (3x+2y=52)-(3x+y=38). You now have y=14.
  • Now plug y=14 into one equation. 3x+2(14)=52
  • Distribute. 3x+28=52
  • Subtract the integer on the left from the integer on the right. 52-28=24
  • You should now have 3x=24. Now divide. 24/3=8
  • y=14 and x=8

This method is okay to use but it will not always be this simple.

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