Question

The charge c of a telephone company is partly constant and partly varies as the number of unit of call, u. The cost of 90 unit is 1120 and cost of 120 unit is 1216 find
A: The formula which connect c and u
B:Find c when u=150 units

Answer 1

$\large\underline{\sf{Solution-}}$

Given that,

The charge c of a telephone company is partly constant and partly varies as the number of unit of call, u.

Let we assume that,

$\rm :\longmapsto\:c = xu + y - - - (i)$

where x and y are arbitrary constants and y is the fixed charges and x be the charges per unit call.

According to statement, it is given that

The cost of 90 unit is 1120

It implies,

Total calling charges, u = 1120

and

Number of units call, u = 90

Hence,

$\rm :\longmapsto\:1120 = 90x + y - - - (1)$

Again, given that cost of 120 unit is 1216.

It implies,

Total calling charges, c = 1216

and

Number of units call, u = 120

Hence,

$\rm :\longmapsto\:1216 = 120x + y - - - (2)$

Now, On Subtracting equation (1) from equation (2), we get

$\rm :\longmapsto\:30x = 96$

$\bf\implies \:x = 3.2$

On substituting the value of x, in equation (1), we get

$\rm :\longmapsto\:1120 = 90 \times 3.2 + y$

$\rm :\longmapsto\:1120 = 288 + y$

$\rm :\longmapsto\:1120 - 288 = y$

$\bf\implies \:y = 832$

So, on substituting the values of x and y, in equation (i),

$\bf :\longmapsto\:c = 3.2u + 832$

So, its the required relationship between c and u.

Now, to find the charges for 150 units,

Substituting the value of u = 150 in above relationship, we get

$\bf :\longmapsto\:c = 3.2(150)+ 832 = 480 + 832 = 1312$

Basic Concept Used :-

Writing Systems of Linear Equation from Word Problem.

1. Understand the problem.

Understand all the words used in stating the problem.

Understand what you are asked to find.

2. Translate the problem to an equation.

Assign a variable (or variables) to represent the unknown.

Clearly state what the variable represents.

3. Carry out the plan and solve the problem.