Question

In a factory, the profit P varies directly with the inventory I. If P = 100 when I = 40, find P when I = 50.

Answer 1

To find the profit P when inventory I is 50, use the direct variation relationship P = kI. Given P = 100 when I = 40, find k and calculate P for I = 50, resulting in a profit of $125.

Step-by-step explanation:

In mathematics, when the profit P varies directly with the inventory I, it means that as the inventory increases, the profit increases proportionally, and this relationship can be expressed as P = kI where k is a constant. To find the value of k, we use the given values P = 100 when I = 40, so k = P/I which gives us k = 100/40 = 2.5. Now that we know k, we can calculate the profit when the inventory is I = 50 using the same direct variation formula: P = kI, so P = 2.5 × 50 = 125. Therefore, the profit P when the inventory I is 50 will be $125.

SUMUP all the final answer as points at last:

• Direct variation relationship between profit and inventory.
• Calculate constant k using initial values of P and I.
• Find new profit at I = 50 using the direct variation formula and constant k.
• The final profit when I is 50 is $125.