ID: 1e11190a
(SAT Suite Question Bank > Find Questions > Assessment: SAT + Test: Math + Domain: Algebra)
Comment: There is the standard way, and then there is the logical way.
Method 1: The question seems designed to get someone to set up and solve a system of equations. However, this is a case in which using the answers might lead to a faster and more comfortable solution. All we need to do is track pints of blackberries. What makes sense within the given information, 4, 5, 8, or 12? When you can focus on a single unknown as opposed to two unknowns simultaneously, the problem becomes much more workable. You might track pints of blackberries in the following way:
Store A: $5.50 per pint
Store B: $8.00 per pint
Because whole numbers are easier to work with than decimals, it would make more sense to focus on Store B first. We can examine Store A later if necessary. Clearly, 12 pints does not make sense, since the total purchase price at Store B, we are told, would be $66.00—8 * 12 > 66, without doing any exact calculations. Get rid of (D). We can eliminate (C) on similar grounds, although we will have to consider raspberries. That is, if someone were to purchase 8 pints of blackberries at Store B, 8 * $8 = $64.00, leaving only $2.00 to purchase raspberries. Since Store B sells raspberries for more than $2.00 per pint, and the passage gives no indication that partial pints may be purchased, (C) cannot be the answer either. Now, if someone were to purchase 5 pints of blackberries at Store B, that would cost 5 * $8.00, or $40.00, leaving $66.00 - $40.00, or $26.00 with which to purchase pints of raspberries. Does $6.50 fit into $26.00 evenly? Yes. 6.5 * 2 = 13, and 13 * 2 = 26. Hang on to this one. All we need to do is test (A), using the same mental math as before:
4 pints of blackberries * $8.00/pint = $32.00
$66.00 - $32.00 = $34.00
$34.00/$6.50 per pint of raspberries = non-integer
In short, (A) cannot be the answer, and we never even had to consider the two stores. The correct answer must be (B), and the process above could lead to the answer in under a minute.
Method 2: Create two equations in Desmos, perhaps using x for (pints of) raspberries and y for blackberries. The point of intersection of the two lines shows a y-value of 5. The correct answer is (B).
Method 3: You could create a system of equations and solve, but why bother when Desmos can do the work for you, even check the answer faster than you could probably set up and solve the system yourself? However, if you like to do things by the book, you could use either substitution or elimination to solve for the unknown in question. You could also use r for raspberries and b for blackberries. Because fractions are harder to work with than whole numbers, why not start by getting rid of the fractions?
5.50r + 3.00b = 37.00 --> 11r + 6b = 74
6.50r + 8.00b = 66.00 --> 13r + 16b = 132
These numbers are getting large really fast, and 11 and 13 do not have a common multiple until 11 * 13, 143, at which point it is probably going to be necessary to use a calculator for the larger numbers.
13(11r + 6b = 74) --> 143r + 78b = 962
11(13r + 16b = 132) --> 143r + 176b = 1,452
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-98b = -490
b = 5
This method is substandard next to the two outlined above. Even so, it is apparent that the correct answer is (B).
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