Hi Mike,

Here is a really confusing question from Applerouth’s SAT text:

a = 1.5 x + 1.50
b = 1.25x + 4.50

In the system of equations above, a and b represent the cost, in dollars, of buying x buffalo wings at two different restaurants. What amount of money will get you the same number of buffalo wings at both restaurants?

A) 12
B) 19.5
C) 20
D) 29.5

The answer is A. No idea how to do this.

You have to find this by looking for the number of wings that costs the same at both stores, so set a and b (the costs at each store) equal to each other and then solve for (the number of wings that will make each store’s cost the same).

1.5x + 1.50 = 1.25x + 4.50
0.25x = 3
x = 12

Therefore, buying 12 wings at each store costs the same amount of money. The question appears to ask HOW MUCH money, so to finish the problem you need to plug 12 back in for x in either of the equations. I’ll do the first one:

a = 1.5(12) + 1.50
a = 19.50

So the answer really should be B. The answer would be A if the question asked for the number of wings that cost the same at both stores, but that’s not what the question asks.

One other note: it might make it more clear what’s going on to graph each line. What the graph below shows is that the price (on the y-axis) is cheaper at store a for up to 12 wings, but store b becomes a better deal for 13 or more wings. At the intersection point—12 wings, $19.50—the same number of wings costs the same amount at both stores.