You bought 555 apples and 444 oranges and your friend bought 555 apples and 555 oranges. He bought 555-444=111 oranges more than you bought.
You paid $10, he paid $11, then he paid $1 more than you paid.
This means that 111 oranges cost $1.
Thus, 444 oranges cost $4 and 555 apples cost $10-$4=$6.
1. If 111 oranges cost $1, then 1 orange cost [tex]\$\dfrac{1}{111} .[/tex]
2. If 555 apples cost $6, then 1 apple cost [tex]\$\dfrac{6}{555}=\dfrac{2}{185}.[/tex]
Answer:
Each apple costs $1.20 and each orange costs $1.
Step-by-step explanation:
Let x represent the number of apples and y represent the number of oranges.
For the fruit you bought, 5 apples and 4 oranges, we have 5x+4y. This costs $10. This gives us the equation
5x+4y = 10
For the fruit your friend bought, 5 apples and 5 oranges, we have 5x+5y. This costs $11. This gives us the equation
5x+5y = 11
Together we have the system
[tex]\left \{ {{5x+4y=10} \atop {5x+5y=11}} \right.[/tex]
We will eliminate x by subtracting the bottom equation from the top:
[tex]\left \{ {{5x+4y=10} \atop {-(5x+5y=11)}} \right. \\\\-1y = -1[/tex]
Divide both sides by -1:
-1y/-1 = -1/-1
y = 1
Each orange costs $1.
Substitute this into the first equation:
5x+4(1) = 10
5x+4 = 10
Subtract 4 from each side:
5x+4-4 = 10-4
5x = 6
Divide both sides by 5:
5x/5 = 6/5
x = 1.2
Each apple costs $1.20.
