Question 101·Medium·Linear Equations in One Variable
A bakery begins the day with 10 pounds of flour. The bakers use the flour at a constant rate of pound every hour. After how many hours will only 1 pound of flour remain? Ѕourсe: аnікo.аі
For word problems involving a constant rate, translate the situation into a simple linear equation using the structure "starting amount − (rate × time) = remaining amount." Define a variable for time, write an expression for how much quantity is left, set it equal to the target amount from the problem, and then solve the linear equation carefully, checking units (pounds vs. hours) and, if there is time, plug your answer back into the original expression to confirm it makes sense.
Hints
Write an expression for flour remaining
If is the number of hours, how can you write an expression for how many pounds of flour are used after hours at a rate of pound per hour? Then subtract that from 10.
Set up the equation
You want to know when the remaining flour is 1 pound. Once you have an expression for the remaining flour, set it equal to 1.
Solve the linear equation
After you set up the equation, combine like terms and isolate the variable by undoing addition/subtraction first, then undoing multiplication by the fraction. аniko.aі/sаt
Think in terms of total flour used
Another way: How many pounds of flour must be used to go from 10 pounds down to 1 pound? At pound per hour, how many hours does it take to use that amount?
Desmos Guide
Enter the equation for remaining flour
In Desmos, type y = 10 - (3/4)x to represent the amount of flour remaining after hours.
Graph the target amount of flour
On a new line, type y = 1 to represent the situation when there is exactly 1 pound of flour left.
Find the intersection
Look for the point where the two graphs intersect. The x-coordinate of this intersection is the number of hours after opening when only 1 pound of flour remains.
Step-by-step Explanation
Define the variable and write an expression for flour remaining
Let be the number of hours after the bakery opens.
Each hour, the bakers use pound of flour. After hours, the total flour used is pounds.
The flour remaining after hours is then:
Set up an equation for when 1 pound remains
We are told to find when only 1 pound remains, so set the expression for remaining flour equal to 1:
Now we just need to solve this linear equation for .
Isolate the term with the variable
First, move the constant term 10 to the other side.
Subtract 10 from both sides:
Solve for the number of hours
To solve , divide both sides by , which is the same as multiplying both sides by :
So it will take hours until only 1 pound of flour remains. Sοurcе: anikо.аі