Store A sells raspberries for $5.50 per pint and blackberries for $3.00 per pint. Store B sells raspberries for $6.50 per pint and blackberries for $8.00 per pint. A certain purchase of raspberries and blackberries would cost $37.00 at Store A or $66.00 at Store B. How many pints of blackberries are in this purchase?

A. 4
B. 5
C. 8
D. 12

You can probably do the above question by plugging in the answers, but is there a more algebraic way to solve it?

Start by setting up equations, using x for pints of raspberries and y for pints of blackberries.

Store A: 5.5x+3y=37
Store B: 6.5x+8y=66

The question asks for pints of blackberries (that’s y) and of course we have a few different ways we know how to solve a system of equations, including the ol’ tried-and-true substitution method. But since the new digital SAT (that’s where this sample question is from, right?) will include the Desmos graphing calculator right on screen, let’s solve this by graphing:

Just type the equations in (no need to even convert them to y= form…) and then hover your mouse over the intersection point. The graph intersects at (4, 5), so y=5, so the answer is B.

We can of course confirm this by plugging (4, 5) back into either or both equations:

Store A:
Looks good!

Store B:
Also looks good!

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