three apples and two ponkans cost P51.00. two apples and three ponkans cost P46.50. how much will half a dozen apples and half a dozen ponkans cost?

To solve this problem, we can set up a system of equations. Let's let "a" represent the cost of one apple and "p" represent the cost of one ponkan.

From the given information, we can create two equations:

Equation 1: 3a + 2p = 51.00
Equation 2: 2a + 3p = 46.50

We now have a system of linear equations. We can solve this system using either substitution or elimination method.

Let's solve it using the elimination method:
1. Multiply Equation 1 by 2 and Equation 2 by 3 to make the coefficients of "a" on both equations equal.
Equation 1: 6a + 4p = 102.00
Equation 2: 6a + 9p = 139.50

2. Subtract Equation 1 from Equation 2 to eliminate "a" and solve for "p."
(6a + 9p) - (6a + 4p) = 139.50 - 102.00
5p = 37.50

3. Divide both sides of the equation by 5 to solve for "p."
p = 37.50 / 5
p = 7.50

Now, we substitute the value of "p" back into either Equation 1 or Equation 2 to solve for "a."

Let's substitute it into Equation 1:
3a + 2p = 51.00
3a + 2(7.50) = 51.00
3a + 15.00 = 51.00
3a = 36.00
a = 36.00 / 3
a = 12.00

Therefore, one apple costs P12.00 and one ponkan costs P7.50.

Finally, to find the cost of half a dozen apples and half a dozen ponkans, we need to multiply the respective prices by their quantities.
Half a dozen is equal to 6. Therefore:

Cost of half a dozen apples = 6 * 12.00
Cost of half a dozen ponkans = 6 * 7.50

Finally, the total cost of half a dozen apples and half a dozen ponkans is the sum of these two quantities.

Cost of half a dozen apples and half a dozen ponkans = (6 * 12.00) + (6 * 7.50)

Calculating this, we get:

Cost of half a dozen apples and half a dozen ponkans = 72.00 + 45.00
Cost of half a dozen apples and half a dozen ponkans = P117.00

Therefore, half a dozen apples and half a dozen ponkans will cost P117.00.

3a + 2p = 51

2a + 3p = 46.5

multiply the first by 3 and the 2nd by 2 to get the p's the same, then
subtract them. Once you have found a, sub it back into the original first
equation to find p
then evaluate 6a + 6p

a = cost of aples

p = cost of ponkans

You must solve system of two equations:

3 a + 2 p = 51

2 a + 3 p = 46.5
____________

The solutions are:

a = 12 , p =7.5

Half a dozen apples and half a dozen ponkans cost:

a / 2 + p / 2 = 12 / 2 + 7.5 / 2 = 6 + 3.75 = 9.75