IBMediumAlgebra7–9

One Cost in Direct Proportion, One Time in Inverse Proportion

Um Custo em Proporcionalidade Direta, Um Tempo em Proporcionalidade Inversa

In a print shop the cost $C$ of a poster is directly proportional to its area $A$ , and a poster of area $2000 \text{ cm}^{2}$ costs $15$ euros. The time $t$ needed to print a large order is inversely proportional to the number $n$ of printers used, and $4$ printers take $9$ hours. Find the cost of a poster of area $3200 \text{ cm}^{2}$ , and the number of printers needed to finish the order in $3$ hours.

Each relationship has its own constant, and both constants are found the same way: substitute the pair of values you are given. What differs is where the variable sits — in one relationship doubling it doubles the other quantity, in the other it halves it.

Solution

Step 1 of 12

1.Direct proportion: $C = kA$ .