Question

What equation in standard form determines the number of violets (x) and the number of orchids (y) Zack can buy?

a) (7x + 12y = 73)
b) (12x + 7y = 73)
c) (x + y = 73)
d) (7x 12y = 73)

Answer 1

It correctly represents the cost of violets (12x) and orchids (7y) with a total cost constraint of $73. The coefficients align with the problem's context. Thus the correct option is b.

Step-by-step explanation:

To find the correct equation, let's consider the problem. The standard form of a linear equation is Ax + By = C, where A, B, and C are constants. In this case, we are looking for an equation that represents the total cost of violets and orchids, with the constraint that the total cost is $73. The correct equation is determined by the coefficients of x and y.

Analyzing option (a), (7x + 12y = 73), the coefficients do not match the problem's context. However, option (b), (12x + 7y = 73), correctly reflects the given scenario. The coefficient 12 represents the cost of violets, and 7 represents the cost of orchids, fitting the problem's context.

Option (c), (x + y = 73), lacks the necessary coefficients for differentiating the costs of violets and orchids. Option (d), (7x 12y = 73), contains a syntax error, and the absence of the plus sign suggests an incorrect representation.

Therefore, the correct equation is (12x + 7y = 73), accurately reflecting the relationship between the number of violets and orchids Zack can buy within the given budget.

Answer 2

The equation (12x + 7y = 73) accurately represents the relationship between the number of violets (x) and orchids (y) Zack can buy in terms of their costs. The coefficients 12 and 7 denote the cost of each violet and orchid, respectively, resulting in a total cost of 73. Thus the correct option is b) (12x + 7y = 73).

Step-by-step explanation:

The correct equation in standard form is (12x + 7y = 73). This can be determined by understanding the problem's context. In the equation, (x) represents the number of violets, (y) represents the number of orchids, and the total cost is 73. The coefficients 12 and 7 represent the cost of each violet and orchid, respectively.

To elaborate, if Zack buys (x) violets and (y) orchids, the total cost can be calculated as (12x + 7y). This expression is then set equal to the total cost of 73, leading to the equation (12x + 7y = 73).

In conclusion, the correct equation is vital for accurately representing the relationship between the number of violets and orchids Zack can buy in terms of their costs.

Therefore, option (b) (12x + 7y = 73) is the correct choice for the standard form equation that determines Zack's floral purchases.