Linear Equations

Question

The total mass of a battery charger, nine 2A and five 3A batteries is 455 g. The total mass of the charger, seven 2A batteries and three 3A batteries is 381 g. It is known that the mass of a 2A battery is 1 g more than twice the mass of a 3A battery. Find the mass of the charger.

Answer 1

Let x = the mass of a 3A battery

Let 3x + 1 = the mass of a 2A battery

Let y = the mass of the charger

 

5x + 9(3x + 1) + y = 455

5x + 27x + 9 + y = 455

32x + y = 446    (equation #1)

 

3x + 7(3x + 1) + y = 381

3x + 21x + 7 + y = 381

24x + y = 374     (equation #2)

 

Subtract Equation 2 from Equation 1.

 32x + y = 446

-24x + y = 374

8x = 72

x = 9

32x + y = 446

32(9) + y = 446

288 + y = 446

y = 158 grams