A certain number of sixes and nines are added to give a sum of 126; if the number of sixes and nines are?

Question

interchange, the new sum is 114. How many of each were there originally? pls. show the solution...thanks

Answer 1

9*X + 6*Y = 126

9*Y + 6*X = 114

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Now solve by the normal methods of solving a system of equations.

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y = (126 - 9X) / 6

9 ((126 - 9X) / 6) + 6 X = 114

X = 10

9 * 10 + 6Y = 126

6Y = 36

Y = 6

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Originally, there were 10 nines and 6 sixes.

Answer 2

The equations should be an X amount of 9s plus a Y amount of 6s equals 126, and a Y amount of 9s plus an X amount of 6s equals 114. So,

9x + 6y = 126

9y + 6x = 114

Then use substitution or whatever you're learning to figure it out. I'm assuming it's homework, so at least solve it from there.