Direct and inverse proportions

Question

The total monthly income, SD, of a salesman who sells tyres consists of a basic salary of $600 and a variable amount which depends on the number of tyres he sells. For each tyre he sells, he receives $8.

(i) If the salesman sells 95 tyres in a particular month, find his total income for that month. (ii) If the salesman's monthly income for a particular month is $1680, calculate the number of tyres he sells in that month.

(iii) Write down a formula connecting D and n, where n is the number of tyres the salesman sells in a month.

(iv) Draw the graph of D against n. Is D directly

proportional to n? Use your graph to explain

your answer.

Answer 1

Hi Jerry,

Lets work through your problem.

The total monthly income, SD, of a salesman who sells tires consists of a basic salary of $600 and a variable amount which depends on the number of tires he sells. For each tire he sells, he receives $8.

Given: Monthly income D is basic Salary 600 and each tire at $8 a tire

We can use this to generate and equation

Based on your word problem, it says to use n for the number of tires that are sold for the month and D for the total Monthly Income.

So Monthly income D is basic Salary 600 and each tire at $8 a tire

is translates to = 600 and means 600 + 8 a tire Means 8n

D = 600 + 8n

(i) If the salesman sells 95 tires in a particular month, find his total income for that month.

So now we can use the equation to answer this part

D= 600 + 8n They tell us we sold 95 tires. How much does it cost. Substitute 95 for n

D=600 + 8(95) = 1360

(ii) If the salesman's monthly income for a particular month is $1680, calculate the number of tires he sells in that month.

D= 600 + 8n Now they give us total monthly income. So substitute 1680 for D

1680 = 600 + 8n Solve for n

1080 = 8n

n = 135

(iii) Write down a formula connecting D and n, where n is the number of tires the salesman sells in a month.

We wrote this down above

D= 600 + 8n

(iv) Draw the graph of D against n. Is D directly

proportional to n? Use your graph to explain

your answer.

The general formula for direct proportion is y=kx where k is the constant of proportionality.

Your Equation is D= 8n + 600 Graph this and see what it looks like.

For direct proportionality, your graph needs to be a straight line that passes through the origin.

Hope this helps!