Final answer:
The cost of apples varies jointly with the number of bags and the price per bag, expressed as c = kbp. Given it costs $30 to buy 4 bags at $5 each, the constant of variation k is 1.5, and the equation is c = 1.5bp.
Step-by-step explanation:
The student's question is about understanding how the cost of buying apples is related to the number of bags and the price per bag, which involves joint variation. In mathematics, when we say that 'y varies jointly as x and z,' we are describing a situation where y = kxz, with k being the constant of variation. In this specific case, the cost (c) varies jointly with the number of bags (b) and the price per bag (p), which is written as c = kbp.
According to the information provided, when it cost $30 to buy 4 bags with each bag costing $5, we can substitute these values into our equation to find the constant of variation. So it would look like this: 30 = k(4)(5). Solving this, we find that k = 30 / (4 * 5), which simplifies to k = 1.5. Therefore, our equation that models the situation is c = 1.5bp.