Question

1. a number is tripled, then 10 is taken away. this gives the same result as if the number were quadrupled. set up and solve an equation to find the original number. (b - 3)

Explanation:

Define the variable

Let \(x\) represent the original unknown number.

Translate the word problem

"A number is tripled" means \(3x\).
"Then 10 is taken away" means \(3x - 10\).
"This gives the same result as if the number were quadrupled" means \(4x\).
Equating these expressions gives the equation:

$$3x - 10 = 4x$$

Solve the equation

Subtract \(3x\) from both sides of the equation to isolate the variable:

$$-10 = 4x - 3x$$

$$x = -10$$

Verify the solution

Triple the number:

$$3 \times (-10) = -30$$

Take away 10:

$$-30 - 10 = -40$$

Quadruple the original number:

$$4 \times (-10) = -40$$

Both sides yield \(-40\), confirming the solution is correct.

Answer:

Equation:

$$3x - 10 = 4x$$

Original number:

$$x = -10$$