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Linear equations in two variables SAT question

Math · Algebra · Hard · Answer it here, explanation included.

The figure presents a scatterplot titled “Number of Cornflowers and Wallflowers at Garden Store.” The horizontal axis is labeled “Number of cornflowers,” and the numbers 0 through 20, in increments of 2, are indicated. The vertical axis is labeled “Number of wallflowers,” and the numbers 0 through 20, in increments of 2, are indicated. There are 5 data points on the graph. The data represented by the points are as follows. Data point 1. Number of cornflowers, 0. Number of wallflowers, 12. Data point 2. Number of cornflowers, 4. Number of wallflowers, 9. Data point 3. Number of cornflowers, 8. Number of wallflowers, 6. Data point 4. Number of cornflowers, 12. Number of wallflowers, 3. Data point 5. Number of cornflowers, 16. Number of wallflowers, 0.

The points plotted in the coordinate plane above represent the possible numbers of wallflowers and cornflowers that someone can buy at the Garden Store in order to spend exactly $24.00 total on the two types of flowers. The price of each wallflower is the same and the price of each cornflower is the same. What is the price, in dollars, of 1 cornflower?

Enter a number or fraction (like 3/17 or 0.176). Press Enter to check.

ExplanationShow

The correct answer is 1.5. The point with coordinates 16 comma 0 corresponds to the situation where 16 cornflowers and 0 wallflowers are purchased. Since the total spent on the two types of flowers is $24.00, it follows that the price of 16 cornflowers is $24.00, and the price of one cornflower is $1.50. Note that 1.5 and 3/2 are examples of ways to enter a correct answer.

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