SOLUTION: how do u solve a typical problem like this one A park ranger spent $104 to buy 12 trees.Redwood trees cost$12 each and spruce trees cost$8 each.How many of each tree did the park r

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Question 190608: how do u solve a typical problem like this one A park ranger spent $104 to buy 12 trees.Redwood trees cost$12 each and spruce trees cost$8 each.How many of each tree did the park ranger buy?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Let
x = # of trees that cost $12

y = # of trees that cost $8


Since he bought 12 trees total, this means that x%2By=12


Also, because "Redwood trees cost$12 each and spruce trees cost$8" and the total came to $104, this tells us that 12x%2B8y=104


So we have the system:


system%28x%2By=12%2C12x%2B8y=104%29


x%2By=12 Start with the first equation.


y=12-x Subtract x from both sides.


y=-x%2B12 Rearrange the terms.


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12x%2B8%28-x%2B12%29=104 Now plug in y=-x%2B12 into the second equation.


12x-8x%2B96=104 Distribute.


4x%2B96=104 Combine like terms on the left side.


4x=104-96 Subtract 96 from both sides.


4x=8 Combine like terms on the right side.


x=%288%29%2F%284%29 Divide both sides by 4 to isolate x.


x=2 Reduce.


So the ranger bought 2 trees that cost $12 a piece.


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Since we know that x=2, we can use this to find y.


y=-x%2B12 Go back to the first isolated equation.


y=-2%2B12 Plug in x=2.


y=10 Combine like terms.


So the ranger bought 10 trees that cost $8 a piece.