Question

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.

Answer 1

The cost of 2 apples is $2.33 and the cost of 1 pear is $1.50.

Step-by-step explanation:

To find the cost of 2 apples and the cost of 1 pear, we need to solve a system of linear equations based on the given information. Let's assign variables to represent the cost of an apple and a pear.

Let's say the cost of 2 apples is 'a' dollars, and the cost of 1 pear is 'p' dollars. From the first week, we have the equation 3a + 8p = 14.50. From the second week, we have the equation 6a + 4p = 14. To solve this system of equations, we can use the method of substitution or elimination.

Using the method of substitution, we can isolate one variable from one equation and substitute it into the other equation. From the second equation, we can isolate 'a' by subtracting 4p from both sides, giving us 6a = 14 - 4p. We can divide both sides by 6 to find a = 2.33 - 0.67p. Substituting this value of 'a' into the first equation, we get 3(2.33 - 0.67p) + 8p = 14.50. Simplifying this equation gives us 6.99 - 2p + 8p = 14.50. Combining like terms, we have 5.01p = 7.51. Dividing both sides by 5.01 gives us p = 1.50.

Therefore, the cost of 2 apples is $2.33 and the cost of 1 pear is $1.50.

Answer 2

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.