Question

for a certain type of heater, the increase in gas bills is directly proportional to the temperature setting (in fahrenheit). if the gas bills increased by $20 when the temperature setting is increased by 4 degrees fahrenheit, by how much will expenses increase when the temperature setting is increased by 10 degrees fahrenheit

Answer 1

The gas bill increases by $50

Explanation:

We know that the increase in gas bills is directly proportional to the temperature setting. Let's take the increase in gas bills as g and increase in temperature setting as t. Thus, this can be written as:

g ∝ t

In every proportionality, there is a constant k, so it will be:

g = kt

It is mentioned that when the temperature setting increases by 4, the gas bill increases by $20, so in terms of the constant, we can write it as:

20 = k 4

We don't know the value of the constant, so we have to first find it out.

k = 20 ÷ 4

k = 5

Thus,

g = 5t

Now that we know the value of the constant, we can find by how much the gas bill will increase if the temperature setting increases by 10.

g = 5 × 10

g = 50

∴ the gas bill increases by $50 when the temperature setting increases by 10 degrees Fahrenheit.