SOLUTION: Hi I need help on knowing how to solve for word problems using systems; Ex: if 4 apples and 2 oranges equals $1 and 2 apples and 3 oranges equals $0.70, how much does each apple an

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Question 663303: Hi I need help on knowing how to solve for word problems using systems; Ex: if 4 apples and 2 oranges equals $1 and 2 apples and 3 oranges equals $0.70, how much does each apple and each orange cost? ... Thanks!
Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
This is a very common type of problem.
Let A be the number of apples and O be the number of oranges.
You are told
4A+%2B+2O+=+100 we are using cents here instead of dollars
2A+%2B+3O+=+70
You have two equations and two unknowns. So you can solve this one
Now you can use your favorite method to solve.
Let's use substitution
4A+%2B+2O+=+100
2A+%2B+O+=+50
O+=+50+-+2A
Now use that and plug it into the second equation as follows
2A+%2B+3O+=+70
2A+%2B+3%2A%2850-2A%29+=+70
2A+%2B+150+-+6A+=+70
-4A+=+-80
A+=+20 so an apple is 20 cents
If an apple it 20 then plug in to find the cost of an orange
4%2A20+%2B+2O+=+100
80+%2B+2O+=+100
2O+=+20
O+=+10 oranges are a dime. Go not sure what store you shop at, but fruit is a steal :)
Check you answer using the second equation. Does
2A+%2B+3O+=+70???