Question

He Brought 10 packages of AA and AAA batteries for a total of 72 batteries.

The AA batteries are sold in packages of 6, and the AAA batteries are sold in packages of 8. Write a system of equations that can be solved to find how many packages of each type of battery Dan bought. Remember to define your variables.
Please answer in full! Thank you

Answer 1

4 packages of AA batteries

6 packages of AAA batteries.

Explanation:

Let the number of packages of AA batteries bought be x

Let

the number of packages of AAA batteries bought be Y

He Brought 10 packages of AA and AAA

thus,

x+y = 10 equation 1

Given

The AA batteries are sold in packages of 6, it means one packet contains 6 batteries

Thus,

Total number of AA batteries in x packages = 6x

The AAA batteries are sold in packages of 8, it means one packet contains 8 batteries

Thus,

Total number of AAA batteries in y packages = 8y

Given total no. of batteries is 72

thus

6x + 8y = 72 equation 2

x+y = 10

y = 10-x ---using this in equation 2

6x + 8(10 - x) = 72

=> 6x + 80 - 8x = 72

=> -2x = 72-80 = -8

=> x = -8/-2 = 4

y = 10 -x = 10 -4 = 6

y = 6

Thus,

he bought 4 packages of AA batteries

6 packages of AAA batteries.