Question

The amount of sales of single scoop ice cream cones the summer as(c) varies directly with the number of customers c twelve customers bought a total of $ 54 worth of ice cream cones which equation can be used to find the ice cream sales for c customers

A) S(c)= 648c
B) S(c)= 4.5c
C) S(c)= 4.5/c
D) S(c)= 648/c

Answer 1

B) S(c)= 4.5c

Explanation:

Here, S(c) represents the sales of ice cream ( in dollars ) for c customers.

∵ Sales of ice cream varies directly with the number of customers,

That is,

S(c) ∝ c

⇒ S(c) = kc ------(1),

Where, k is proportionality constant.

Now, 12 customers bought a total of $ 54 worth of ice cream cones,

i.e. S(c) = 54 if c = 12

From equation (1),

`54 = 12c`

`\implies c = (54)/(12)= 4.5`

Again by equation (1),

The required equation would be,

S(c) = 4.5c

i.e. OPTION B is correct.

Answer 2

Option B is correct.

S(c) = 4.5c where c is the number of customers

Explanation:

Direct variation states a relationship between two variables in which one is a constant multiple of the other.

In other words, when one variable changes the other changes in proportion to the first.

If y is directly proportional to x, i,e
`y \propto x`

then the equation is of the form : y = kx where k is the constant variation.

Given: 12 customers bought a total of $ 54 ice cream.

Let s(c) be the amount of sales of cream cones the summer and c be the number of customers.

then as per the condition;

`S(c) \propto c`

By definition of direct variation:

`S(c) = kc`

Substitute the value of c = 12 customers and S(c) = $ 54 to solve for k;

54 = 12 k

Divide both sides by 12 we get;

`(54)/(12) = (12k)/(12)`

Simplify:

k = 4.5

Therefore, the equation can be used to find the ice cream sales for c customers is; S(c)= 4.5c