Set this equal to 150: - High Altitude Science

Understanding the Context

What Does It Mean to Set an Expression Equal to 150?

When you see an equation like set this equal to 150, you’re dealing with a statement of equivalence. The goal is to isolate the variable to find what number (or expression) makes the entire left side equal exactly 150. This setup appears frequently in math and applied disciplines because 150 often represents a target, limit, or benchmark value.

For example:
- Set the expression \( x + 45 \) equal to 150.
- Find the value of \( y \) such that \( 3y = 150 \).

In both cases, the equation expression = 150 asks, “What value does X need to take so that when plugged into this expression, the result is 150?”

Key Insights

How to Set and Solve Equations Equal to 150

Step 1: Write the Equation
Start by expressing the relationship algebraically. For instance:
\[
x + 45 = 150
\]

Step 2: Isolate the Variable
To solve for \( x \), subtract 45 from both sides:
\[
x + 45 - 45 = 150 - 45
\]
\[
x = 105
\]

Final Thoughts

Practical Examples & Applications

1. Budgeting:
Imagine you have $150 to spend on snacks and drinks. If drinks cost $45, how much can you spend on snacks?
Set up the equation:
\[
\ ext{Snack money} + 45 = 150
\]
\[
\ ext{Snack money} = 150 - 45 = 105
\]
You can buy snacks with $105.

2. Science & Measurement:
Suppose a recipe requires a total mixture volume of 150 mL, and 45 mL is already liquid. How much more solid or dry ingredient do you need?
\[
x + 45 = 150 \implies x = 105 \ ext{ mL}
\]

Tips for Quick Solving

• Always aim to isolate the variable by undoing addition/subtraction with inverse operations.
  - Balance both sides of the equation to maintain equality.
  - Check your solution by substituting back into the original expression.