One week Beth bought 3 apples and 8 pears for $14.50. The next week she bought 6 apples and 4 pears and paid $14. Find the cost of 2 apple and the cost of 1 pear.

Let us assume the cost of 1 apple = x dollars

Let us also assume the cost of 1 pear = y dollars

Then we can form two equations from the details given in the question. Based on those details the required answer to the question can be easily deduced.

3x + 8y = 14.50

And

6x + 4y = 14

Dividing both sides of the equation by 2 we get

3x + 2y = 7

2y = 7 - 3x

y = (7 - 3x) / 2

Putting the value of y from the second equation in the first equation we get

3x + 8y = 14.50

3x + 8[ (7 - 3x) / 2] = 14.50

3x + 4 (7 - 3x) = 14.50

3x + 28 - 12x = 14.50

- 9x = 14.50 - 28

- 9x = - 13.5

9x = 13.5

x = 13.5/9

= 1.5

Putting the value of x in the second equation we get

6x + 4y = 14

(6 * 1.5) + 4y = 14

9 + 4y = 14

4y = 14 - 9

4y = 5

y = 5/4

= 1.25

So we can find from the above deduction that the cost of 1 apple is 1.5 dollars and the cost of 1 pear is 1.25 dollars

Then

Cost of 2 apples = 2 * 1.5 dollars

= 3.0 dollars

So the cost of 2 apples is $3 and the cost of 1 pear is $1.25.