SAT II Math I : Word Problems

Study concepts, example questions & explanations for SAT II Math I

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Example Questions

Example Question #1 : Solving Functions From Word Problems

At Joe's pizzeria a pizza costs $5 with the first topping, and then an additional 75 cents for each additional topping.

If \displaystyle x represents the number of toppings on a pizza, what function represents the cost of a pizza with at least one topping?

Possible Answers:

\displaystyle f(x) = 0.75(x - 1)+5

\displaystyle f(x) = 5 + 75(x-1)

\displaystyle f(x) = 5 + 75x

\displaystyle f(x) = 5x + 0.75

\displaystyle f(x) = 0.75 + 5(x+1)

Correct answer:

\displaystyle f(x) = 0.75(x - 1)+5

Explanation:

Notice that the question describes a linear equation because there is a constant rate of change (the cost per topping). This means we can use slope intercept form to describe the scenario. 

Recall that slope intercept form is

\displaystyle y = mx + b

The value of \displaystyle b is the \displaystyle y-value when \displaystyle x = 0. In this case \displaystyle x=0 means there are zero additional toppings and the question tells us that this pizza costs $5 so:

\displaystyle 5=m(0) +b

\displaystyle 5=b

\displaystyle m is the slope, or rate of change as \displaystyle x increases. In this case each additional topping costs \displaystyle 75 cents. Notice that the units have shifted from dollars to cents so we must write this as \displaystyle 0.75

\displaystyle m=0.75

Notice that the first topping is included in the $5 cost. The \displaystyle 75 cent charge only applies to additional toppings. So one less than the number of toppings is equivalent to:

\displaystyle x-1

Putting all these steps together we get:

\displaystyle 0.75 (x-1) +5

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