Tim bought 3 large popcorn buckets and 2 small drinks for $21. Lisa bought 2 large popcorn buckets and 4 small drinks for $22. How much would 1 large popcorn bucket and 1 small drink cost?

Question

1. Solving Systems of Equations
2. Using Elimination

Answer 1

3p + 2d = 21

2p + 4d = 22

Ok, elimination was very confusing to me at first. We can multiply an equation by a constant and the graph wouldn't change.

3x + 4y = 12 and 9x + 12y = 36 would give us the same graph, for example.

Now, we need one of the variables to have opposite coefficients so that when we add the two equations together, that variable cancels out, like 5t + (-5t). Hey, that's 0, so it cancels out!

Sometimes we can multiply just one of the equations, though sometimes we may need to do both. The trick is to find the LCM of the two coefficients (we can pick either variable) and figure out what we need to multioly each equation by to end up with opposites of that LCM.

Well, hey, if we look at the d, the LCM of 2 and 4 is 4. If we multiply the top equation by -2, we end up with -4d + 4d, right?

-2(3p + 2d) = (21)-2

2p + 4d = 22

-6p - 4d = -42

2p + 4d = 22

Adding the two together, we get...

-4p = -20

p = 5

Now, substitute our value for p into either equation and solve for d.

You got this!

Answer 2

You know the cost of 3 popcorns and 2 drink.

What would be the cost of 6 popcorns and 4 drinks?

From that answer can you figure out the cost of 4 popcorns? Then the cost of a popcorn? Then the cost of a drink?