Question

Model with Mathematics

The owner of a frozen yogurt stand considers different pricing options for a serving of yogurt plus toppings. For what number of toppings do the two options give the same price?
A. Define the variables.
B. Write a system of equations that models this situation.
C. Graph the system. What is the intersection point?
D. What is the solution of the problem?
E. Is the solution reasonable for this situation? Explain.

Answer 1

Explanation:

A, B: Define the Variables and Write Equations

Let T be the number of toppings.

Option 1: $3 + $0.75*T

Option 2: $4 + $0.50*T

C. Graph the System

See the attached graph. The intersection point is (4,6). This means that 4 toppings will result in a cost of $6 for both yogurt options.

D. Solution to the Problem

The solution is given above, but we can also solve using equations, instead of graphing. We want the value of T that will make these expressions equal:

$3 + $0.75*T = $4 + $0.50*T

$0.25*T = $1

T = 4 toppings

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CHECK:

For 4 toppings:

Option 1: $3 + $0.75*T

$3 + $0.75*(4)

$3 + $3 = $6

Option 2: $4 + $0.50*T

$4 + $0.50*(4)

$4 + $2 = $6

Four toppings will make both options equal in cost.

E: Is the solution reasonable?

Yes. The cheaper option ($3) has a more expensive topping, so at some point (at 4 toppings) it will be the same price as the second option, with a higher initial price, but with cheaper toppings.