Question: for the school math week, grade 10 students 3 notebooks costing ₱x a each, but every notebook has a 2 bundles of markers with each bundle costing (₱x + ₱5) to be used during the event. They also purchased I roll a decorative ribbon worth ₱7.question: write and simplify the algebraic expressions that represents the total amount spent by the class.Given: 4(3x- 2) + 2(x + 5) +7 = 12x -8+2% +10+7 Variables: 12x + 2x = 14xConstants: -8 + 10+7=9final answer: 14x +9Is this right?
1. **State the problem:**
We need to write and simplify the algebraic expression representing the total amount spent by the class buying notebooks, marker bundles, and a decorative ribbon.
2. **Define variables and costs:**
- Number of notebooks: $3$
- Cost per notebook: $x$
- Each notebook comes with $2$ bundles of markers
- Cost per marker bundle: $x + 5$
- Decorative ribbon cost: $7$
3. **Write the expression for each item:**
- Total cost of notebooks: $$3 \times x = 3x$$
- Total bundles of markers: $$3 \times 2 = 6$$ bundles
- Total cost of markers: $$6 \times (x + 5) = 6x + 30$$
- Cost of ribbon: $$7$$
4. **Write the total cost expression:**
$$\text{Total} = 3x + (6x + 30) + 7$$
5. **Simplify the expression:**
$$3x + 6x + 30 + 7 = 9x + 37$$
6. **Check the given expression:**
The user gave $$4(3x - 2) + 2(x + 5) + 7$$ which expands to:
$$4 \times 3x - 4 \times 2 + 2x + 10 + 7 = 12x - 8 + 2x + 10 + 7$$
Combine like terms:
$$12x + 2x = 14x$$
$$-8 + 10 + 7 = 9$$
So the simplified expression is:
$$14x + 9$$
7. **Compare both results:**
- Our correct total is $$9x + 37$$
- The user's expression $$14x + 9$$ does not match the problem's conditions.
**Conclusion:** The user's expression is incorrect based on the problem statement.
**Final answer:** $$9x + 37$$