Photography World has a portrait special. A three-pose portrait package has a sitting fee of $35, and a six-pose package has a sitting fee of $60. On a Saturday, $690 was collected in sitting fees. Which equation can be used to represent $x$, the number of three-pose portrait packages and $y$, the number of six-pose portrait packages?
A. $360x + 105y = 690
B. $35x + 60y = 690
C. $105x + 360y = 690
D. $60x + 35y = 690
Answer (2)
Define variables: x is the number of three-pose packages, y is the number of six-pose packages.
Calculate total fees from three-pose packages: 35 x .
Calculate total fees from six-pose packages: 60 y .
Formulate the equation: 35 x + 60 y = 690 . The answer is 35 x + 60 y = 690 .
Explanation
Problem Analysis Let's analyze the problem. We are given the sitting fees for two types of portrait packages and the total amount collected. We need to find the equation that represents the relationship between the number of each type of package and the total amount collected.
Setting up the Equation Let x be the number of three-pose portrait packages and y be the number of six-pose portrait packages. The sitting fee for a three-pose package is $35 , so the total sitting fees from three-pose packages is 35 x . The sitting fee for a six-pose package is $60 , so the total sitting fees from six-pose packages is 60 y . The total sitting fees collected is $690 . Therefore, the equation representing the total sitting fees is: 35 x + 60 y = 690
Final Equation The equation that represents the total sitting fees collected on Saturday is 35 x + 60 y = 690 .
Examples
This type of problem is useful in business for calculating revenue based on the number of different products or services sold. For example, a bakery sells cakes for $25 and cookies for $5 . If the bakery wants to make $500 in a day, they can use the equation 25 x + 5 y = 500 to determine how many cakes ( x ) and cookies ( y ) they need to sell.
The equation that represents the total sitting fees collected for three-pose and six-pose portrait packages is 35 x + 60 y = 690 . Therefore, the correct answer is option B. This equation sums up the fees from both types of packages to equal the total amount collected.
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