At a local orchard, visitors pay an entrance fee of \2.50 per pound of apples picked. The total cost, in dollars, is modeled by the function , where is the number of pounds of apples picked. If a visitor spends exactly \$28, how many pounds of apples did the visitor pick?

Solution available with step-by-step explanation

SAT Linear Functions Question 130 | Free SAT Prep | Aniko

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Question 130·Easy·Linear Functions

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At a local orchard, visitors pay an entrance fee of $3 plus $2.50 per pound of apples picked. The total cost, in dollars, is modeled by the function $g(p) = 3 + 2.5p$ , where $p$ is the number of pounds of apples picked. If a visitor spends exactly $28, how many pounds of apples did the visitor pick?

Your answer

(Express the answer as an integer)

For linear-function word problems on the SAT, first identify what each part of the function represents (fixed fee vs. per-unit rate), then set the function equal to the given total and solve the resulting one-step or two-step linear equation. Work systematically: subtract any constant term (fixed fee) from both sides, then divide by the coefficient of the variable (rate per unit), and sanity-check that your answer makes sense in the context (the number of units should be positive and realistic).

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Use the cost formula

The function $g(p) = 3 + 2.5p$ gives the total cost in dollars for $p$ pounds of apples. You are told the total cost is 28 dollars. How can you use that in an equation?

Isolate the variable step by step

Once you set $3 + 2.5p$ equal to 28, first remove the 3 by doing the opposite operation to both sides. What do you get for the term with $p$ ?

Undo the multiplication

After you isolate the $2.5p$ term, you will have an equation like $2.5p = \text{(some number)}$ . What operation will isolate $p$ ?

Desmos Guide

Enter the total cost equation

In Desmos, type y = 3 + 2.5x to represent the total cost as a function of pounds of apples (using $x$ instead of $p$ ).

Represent the given total cost

On a new line, type y = 28 to show the horizontal line for a total cost of 28 dollars.

Find the number of pounds from the intersection

Look at the point where the two graphs intersect. The $x$ -coordinate of this intersection is the number of pounds of apples that give a total cost of 28 dollars.

Step-by-step Explanation

Translate the situation into an equation

The total cost is modeled by $g(p) = 3 + 2.5p$ , and the visitor spends exactly $28. So set the equation:

3 + 2.5p = 28

Isolate the term with $p$

Subtract 3 (the entrance fee) from both sides to get the cost of just the apples:

\begin{aligned} 3 + 2.5p - 3 &= 28 - 3 \\ 2.5p &= 25 \end{aligned}

Solve for $p$

Now divide both sides by $2.5$ to find $p$ :

\begin{aligned} \frac{2.5p}{2.5} &= \frac{25}{2.5} \\ p &= 10 \end{aligned}

So the visitor picked $10$ pounds of apples.

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Desmos Guide

Step-by-step Explanation

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Strategy

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Desmos Guide

Step-by-step Explanation