SAT Linear Functions Question 105 | Free SAT Prep | Aniko

00:00

Question 105·Hard·Linear Functions

0 / 140

During a laboratory test, the temperature $T$ , in degrees Celsius, of a heated solution is predicted by the linear model

T(t)=90-2\bigl(t-3\bigr),

where $t$ is the time, in minutes, after the test begins. For safety reasons, the experiment must be stopped when the temperature first reaches exactly $60$ degrees Celsius.

According to the model, how many minutes after the test begins should the experiment be stopped?

For SAT questions with a linear model and a target value, immediately set the model equal to the given target and solve the resulting linear equation for the variable. Distribute carefully (especially with negative numbers), combine like terms to get a simple two-step equation, and then isolate the variable using inverse operations. Finally, interpret the solution in context—check units (like minutes) and confirm that your answer matches what the question is asking (for example, “when it first reaches” a certain value).

Hints

Click me!

Use the given model

The model gives $T(t)=90-2(t-3)$ . What equation should you write if you want the temperature $T$ to be exactly $60$ degrees?

Be careful distributing the -2

When you simplify $90 - 2(t - 3)$ , remember that the $-2$ multiplies both $t$ and $-3$ . What do you get for $-2 \cdot t$ and for $-2 \cdot (-3)$ ?

Solve for t step by step

After simplifying, you will have an equation of the form $a + bt = 60$ . Use inverse operations (subtract, then divide) to isolate $t$ .

Remember what t represents

Once you get a value for $t$ , think about the units in the problem. What does $t$ measure in this context?

Desmos Guide

Enter the temperature model

In Desmos, type the equation y = 90 - 2(x - 3) to graph the temperature of the solution as a function of time.

Graph the target temperature

On a new line, type y = 60 to graph a horizontal line representing the safe temperature.

Find the intersection

Click or tap on the point where the two graphs intersect. The x-coordinate of this point is the time in minutes when the temperature reaches 60 degrees according to the model; use that x-value as your answer.

Step-by-step Explanation

Translate the condition into an equation

We are told to stop the experiment when the temperature first reaches exactly $60$ degrees.

So, using the model $T(t)=90-2(t-3)$ , set $T(t)$ equal to $60$ :

90 - 2(t - 3) = 60.

Simplify the expression on the left

Distribute the $-2$ across $(t - 3)$ :

First compute $-2 \cdot t = -2t$
Then compute $-2 \cdot (-3) = +6$

So the left side becomes:

90 - 2(t - 3) = 90 - 2t + 6 = 96 - 2t.

Now the equation is:

96 - 2t = 60.

Solve the linear equation for t

Isolate $t$ step by step.

Subtract $96$ from both sides:

\begin{aligned} 96 - 2t - 96 &= 60 - 96 \\ -2t &= -36 \end{aligned}

Now divide both sides by $-2$ to solve for $t$ :

\begin{aligned} \frac{-2t}{-2} &= \frac{-36}{-2} \end{aligned}

Interpret the solution

Dividing both sides by $-2$ gives $t = 18$ . The variable $t$ represents the time in minutes after the test begins. Since we found $t = 18$ , the experiment should be stopped 18 minutes after it starts, which matches answer choice C) 18.

Strategy

Hints

Desmos Guide

Step-by-step Explanation

Study Hints

Strategy

Hints

Desmos Guide

Step-by-step Explanation