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Hector used a tool called an auger to remove corn from a storage bin at a constant rate. The bin contained 24,000 bushels of corn when Hector began to use the auger. After 5 hours of using the auger, 19,350 bushels of corn remained in the bin. If the auger continues to remove corn at this rate, what is the total number of hours Hector will have been using the auger when 12,840 bushels of corn remain in the bin?

What value of $p$ satisfies the equation $5p+180=250$?

$4x+5=165$

What is the solution to the given equation?

John paid a total of $\$165$ for a microscope by making a down payment of $\$37$ plus $p$ monthly payments of $\$16$ each. Which of the following equations represents this situation?

$3x+21=3x+k$

In the given equation, $k$ is a constant. The equation has infinitely many solutions. What is the value of $k$?

If x is the solution to the equation above, what is the value of ?

Alan drives an average of 100 miles each week. His car can travel an average of 25 miles per gallon of gasoline. Alan would like to reduce his weekly expenditure on gasoline by $5. Assuming gasoline costs $4 per gallon, which equation can Alan use to determine how many fewer average miles, m, he should drive each week?

A tree had a height of 6 feet when it was planted. The equation above can be used to find how many years n it took the tree to reach a height of 14 feet. Which of the following is the best interpretation of the number 2 in this context?

$2x+16=a\left(x+8\right)$

In the given equation, $a$ is a constant. If the equation has infinitely many solutions, what is the value of $a$?

If $\frac{x}{8}=5$, what is the value of $\frac{8}{x}$?

The perimeter of an isosceles triangle is $83$ inches. Each of the two congruent sides of the triangle has a length of $24$ inches. What is the length, in inches, of the third side?

In the given equation, b is a constant. If the equation has no solution, what is the value of b ?

How many solutions does the equation $10\left(15x-9\right)=-15\left(6-10x\right)$ have?

In the equation above, what is the value of x ?

$3(kx+13)=\frac{48}{17}x+36$

In the given equation, $k$ is a constant. The equation has no solution. What is the value of $k$?

Which of the following is equivalent to ?

One pound of grapes costs $2. At this rate, how many dollars will c pounds of grapes cost?

A principal used a total of $25$ flags that were either blue or yellow for field day. The principal used $20$ blue flags. How many yellow flags were used?

$8x=88$

What value of $x$ is the solution to the given equation?

A certain product costs a company $65 to make. The product is sold by a salesperson who earns a commission that is equal to 20% of the sales price of the product. The profit the company makes for each unit is equal to the sales price minus the combined cost of making the product and the commission. If the sales price of the product is $100, which of the following equations gives the number of units, u, of the product the company sold to make a profit of $6,840 ?

$3$ more than $8$ times a number $x$ is equal to $83$. Which equation represents this situation?

In the equation above, a and b are constants. If the equation has infinitely many solutions, what are the values of a and b ?

$4x+6=18$

Which equation has the same solution as the given equation?

$2\left(kx-n\right)=-\frac{28}{15}x-\frac{36}{19}$

In the given equation, $k$ and $n$ are constants and $n>1$. The equation has no solution. What is the value of $k$?

An agricultural scientist studying the growth of corn plants recorded the height of a corn plant at the beginning of a study and the height of the plant each day for the next 12 days. The scientist found that the height of the plant increased by an average of 1.20 centimeters per day for the 12 days. If the height of the plant on the last day of the study was 36.8 centimeters, what was the height, in centimeters, of the corn plant at the beginning of the study?