To solve this problem, we need to write an inequality that describes how long it will take Briyana to save enough money for her spring break trip.
1. Understand the Given Information:
- Initial savings: \[tex]$150
- Saving goal: at least \$[/tex]560
- Weekly savings: \[tex]$45
2. Define the Variable:
- Let \( w \) represent the number of weeks Briyana saves money.
3. Write the Total Savings Equation:
- After \( w \) weeks, Briyana's total savings will be the sum of her initial savings plus the amount she saves each week multiplied by the number of weeks. The total savings can be written as:
\[
150 + 45w
\]
4. Set Up the Inequality:
- Briyana needs her total savings to be at least \$[/tex]560. This means the total savings should be greater than or equal to \$560. The inequality will be:
[tex]\[
150 + 45w \geq 560
\][/tex]
5. Identify the Correct Inequality:
- Comparing with the provided options, the correct inequality that describes this situation is:
[tex]\[
45w + 150 \geq 560
\][/tex]
Therefore, the correct inequality is:
[tex]\[ 45w + 150 \geq 560 \][/tex]
