Question

At imelda's fruit stand, you bought 555 apples and 444 oranges for \$10$10dollar sign, 10, and your friend bought 555 apples and 555 oranges for \$11$11dollar sign, 11.

using this information, is it possible to determine the cost of one apple and one orange from the fruit stand? If so, what do they cost? If not, why not?

Answer 1

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
`\$(1)/(111) .`

2. If 555 apples cost $6, then 1 apple cost
`\$(6)/(555)=(2)/(185).`

Answer 2

Each apple costs $1.20 and each orange costs $1.

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

`\left \{ {{5x+4y=10} \atop {5x+5y=11}} \right.`

We will eliminate x by subtracting the bottom equation from the top:

`\left \{ {{5x+4y=10} \atop {-(5x+5y=11)}} \right. \\\\-1y = -1`

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.