Question

James bought 5 apples and 10 oranges for $4. Emily bought 3 apples and 9 oranges for $3. The shoekeeper strictly told that there would not be any discount. What is the cost of an apple and an orange?

Answer 1

Apple: 40 cents; orange: 20 cents

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.