A bottle 150 vitamins costs $5.25. If the cost varies directly with the number of vitamins in the bottle, what should, how a bottle with 250 vitamins costs?
I need some help .
I don't understand it.
How much does one vitamin cost?
To determine the cost of a bottle with 250 vitamins, we can use the concept of direct variation.
The given information states that the cost varies directly with the number of vitamins. This means that the cost per vitamin is constant. Let's calculate the cost per vitamin:
Cost per vitamin = Total cost / Number of vitamins
Cost per vitamin = $5.25 / 150 vitamins
Now, we can calculate the cost of a bottle with 250 vitamins by multiplying the cost per vitamin by the number of vitamins:
Cost of a bottle with 250 vitamins = Cost per vitamin * 250 vitamins
Substituting the value of the cost per vitamin, we have:
Cost of a bottle with 250 vitamins = ($5.25 / 150 vitamins) * 250 vitamins
Calculating this expression:
Cost of a bottle with 250 vitamins = $0.035 * 250
Cost of a bottle with 250 vitamins = $8.75
Therefore, a bottle with 250 vitamins would cost $8.75.
To solve this problem, we need to understand the concept of direct variation. In direct variation, when one variable increases, the other variable also increases by the same factor.
In this case, the cost of the vitamins varies directly with the number of vitamins in the bottle. Let's represent the cost as C and the number of vitamins as V. So we have the equation C = k * V, where k is the constant of variation.
To find the value of k, we can use the given information: a bottle with 150 vitamins costs $5.25. Plugging this into the equation, we have 5.25 = k * 150.
To solve for k, divide both sides of the equation by 150: k = 5.25 / 150. Evaluating this gives k = 0.035.
Now, to find the cost of a bottle with 250 vitamins, we can substitute V = 250 and k = 0.035 into the equation C = k * V: C = 0.035 * 250.
Calculating this gives us C = $8.75.
Therefore, a bottle with 250 vitamins would cost $8.75.