Tameka bought 50 cans of soda ( cola, grape, and orange) to serve at a party. She has 8 more colas than grape sodas, and 3 less orange sodas than grape sodas. How many of each type of soda did Tameka buy?

We want to get a variable all by itself in an equation so first I'm going to put the second equation (R + 3 = G) in the first (8 + G = C) by replacing the G to get

8 + (R + 3) = C Combine the variables 11 + R = C and put that new equation into the last equation

(11 + R) + G + R = 50

Now plug our original second equation (R + 3 = G) into our third to get

(11 + R) + (R + 3) + R = 50

Combine and get

14 + 3R = 50 Subtract over the 14

3R = 36 Divide by 3

Orange Sodas = 12

Our new 3rd Equation is now: C + G + 12 = 50, subtract over 12 to get

C + G = 38

Plug either equation 1 or 2 into that one, I'll do 1

(8 + G) + G = 38

8 + 2G = 38

2G = 30

Grape Sodas = 15

Now our 3rd equation is C + 15 = 38, subtract over 15

Cola Sodas = 23

Orange = 12

Grape = 15

Cola = 23

12 + 15 + 23 = 50