I am donating packages for Christmas drive. After the first week, I spent 126 to donate three children packages and 8 adult packages. After two weeks I spent 108 to donate six children packages and 4 adult packages. What is the price of each type of package

Step-by-step explanation:

Let the price for children and adults package be represented with x and y respectively.

For the first week the sum of the package will be as follows:

3x+8y = 126

For the two weeks after:

6x+4y = 108

So, we will be having two equations

3x+8y = 126 ... (1)

6x+4y = 108 ... (2)

These are simultaneous equations

From equation 1

3x+8y = 126

3x = 126-8y

X = 126-8y/3 ... (3)

Put equation 3 into 2

6 (126-8y) / 3 + 4y = 108

756-48y/3 + 4y = 108

756-48y+12y/3 = 108

Cross multiplying

756-48y+12y = 108*3

756-48y + 12y = 324

Collecting like terms

756-324 = 48y-12y

432 = 36y

Divide both sides by 36

432/36 = 36y/36

y = 12

Substituting y into equation 1

3x+8 = 126

3x+96=126

3x = 126-96

3x = 30

Divide both sides by 3

3x/3 = 30/3

x = 10

Hence for each of the packages for children and adults. It will be 10 and 12 respectively.