Question 101·Medium·Linear Functions
A nutrition researcher found that during a moderate indoor-cycling session, the number of calories burned, , can be modeled by the linear equation
where is the number of minutes spent cycling () and is the total calories burned.
If a participant burned 235 calories during a session, which of the following is closest to the predicted number of minutes the participant spent cycling?
For linear function questions like this, first identify which variable you are given and which you need to find. Substitute the known value into the equation, then solve the resulting one-step or two-step linear equation (usually by undoing addition/subtraction, then multiplication/division). Finally, if your solution is a decimal, quickly round or compare it to the answer choices to pick the closest option, and use a quick check by plugging your choice back into the original equation if time allows.
Hints
Use the given equation
You are given a model . Think about which value (calories or minutes) you know and which one you need to find.
Set up an equation with one variable
Replace with 235 in the equation, since 235 is the total calories burned, and then write the new equation involving only .
Solve and then compare to the choices
After you solve the equation for , you will get a decimal number of minutes. Look at the four answer choices and decide which one is closest to that decimal.
Desmos Guide
Compute the minutes directly
In Desmos, type (235 - 70) / 9.4 into the expression line. The output is the predicted number of minutes; then choose the answer choice that is closest to this value.
Step-by-step Explanation
Substitute the given calories into the equation
You are told the participant burned 235 calories, so set in the model:
Now you have an equation with just one variable, , which represents the number of minutes.
Isolate the term with
Subtract 70 from both sides to move the constant term:
Now is by itself on the right-hand side.
Solve for and pick the closest choice
Divide both sides by to solve for :
Use division (or a calculator) to approximate this value: minutes. The answer choice that is closest to is 18, so the predicted number of minutes spent cycling is 18.