Answer:
Apple: 40 cents; orange: 20 cents
Step-by-step explanation:
Use variable a to represent the cost of an apple, and variable o to represent the cost of an orange.
We are told that 5 apples and 10 oranges costs $4.
So 5a + 10o = $4.
We are also told that 3 apples and 9 oranges costs $3.
So 3a + 9o = $3.
Now, we can subtract the equations:
5a + 10o = 4
- (3a + 9o = 3)
-------------------------
2a + o = 1
Isolate variable o.
o = -2a + 1
Substitute o = -2a + 1 into an original equation. We do this so that there is only one variable left in the equation, so we can solve for the variable.
5a + 10o = 4
5a + 10(-2a + 1) = 4
Solve for a.
5a - 20a + 10 = 4
-15a + 10 = 4
-15a = -6
15a = 6
a = 6/15 = 0.40
Now we know that an apple costs 0.40 dollars, or 40 cents.
Substitute a = 0.4 into an original equation to find o.
5a + 10o = 4
5(0.4) + 10o = 4
Solve for o.
2 + 10o = 4
10o = 2
o = 2/10 = 0.20
Now we know that an orange costs 0.20 dollars, or 20 cents.
