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Let's go through the questions one by one.

**1.** If $\frac{3}{4}a + \frac{2}{3}b = 7$, what is the value of $9a + 8b$?

We can multiply both sides of the equation by 12 to eliminate the fractions:
\[
12 \times \left( \frac{3}{4}a + \frac{2}{3}b \right) = 12 \times 7
\]
\[
9a + 8b = 84
\]
So, the value of $9a + 8b$ is **84**. The correct answer is **C**.

---

**2.** Raj can exchange 15 Euros for 11 British Pounds. At this exchange rate, how many British Pounds should he receive for 100 Euros?

We set up a proportion based on the given exchange rate:
\[
\frac{15}{11} = \frac{100}{x}
\]
Cross-multiply:
\[
15x = 1100 \quad \Rightarrow \quad x = \frac{1100}{15} = 73.33
\]
Thus, the closest value is **73**. The correct answer is **B**.

---

**3.** If $ax + b = cx + d$, which gives the value of $x$ in terms of $a$, $b$, $c$, and $d$?

First, solve for $x$:
\[
ax + b = cx + d
\]
\[
ax - cx = d - b
\]
\[
x(a - c) = d - b
\]
\[
x = \frac{d - b}{a - c}
\]
So, the correct answer is **D**.

---

**4.** Jeff received a gift card worth $50 to use on music and movies. Each song costs $1.25, and each movie costs $3. If Jeff downloads 4 songs and 1 movie each month, which equation represents the remaining value of his gift card after $m$ months?

Let $d$ be the amount remaining after $m$ months. In each month, Jeff spends:
\[
4 \times 1.25 + 3 = 5 + 3 = 8 \text{ dollars per month}.
\]
Thus, after $m$ months, he will have spent $8m$, leaving:
\[
d = 50 - 8m.
\]
So, the correct answer is **C**.

---

**5.** Based on the system of equations $2x + y = 3x + 4$ and $x + 5y = 2$, what is the value of $x + y$?

First, solve the first equation:
\[
2x + y = 3x + 4 \quad \Rightarrow \quad y = x + 4.
\]
Substitute into the second equation:
\[
x + 5(x + 4) = 2
\]
\[
x + 5x + 20 = 2 \quad \Rightarrow \quad 6x + 20 = 2 \quad \Rightarrow \quad 6x = -18 \quad \Rightarrow \quad x = -3.
\]
Now, substitute $x = -3$ into $y = x + 4$:
\[
y = -3 + 4 = 1.
\]
So, $x + y = -3 + 1 = -2$. The correct answer is **B**.

---

**6.** A bag of apples and oranges contains twice as many apples as oranges. If there are 15 total pieces of fruit, how many apples are in the bag?

Let $x$ be the number of oranges, and $2x$ be the number of apples. The total number of fruits is:
\[
x + 2x = 15 \quad \Rightarrow \quad 3x = 15 \quad \Rightarrow \quad x = 5.
\]
So, the number of apples is $2x = 2 \times 5 = 10$. Thus, there are **10 apples**.

---

Would you like more details on any of these questions?

Here are 5 related questions:
1. What would happen if the number of oranges increased in question 6?
2. Can you solve a system of equations with three variables like in question 5?
3. How do exchange rates fluctuate and affect calculations like in question 2?
4. How can we adjust the formula in question 4 if the cost of songs or movies changes?
5. How would the answer to question 3 change if the variables were squared?

**Tip:** Always try simplifying equations step by step to avoid errors, especially when working with multiple terms.

If 3/4a + 2/3b = 7, what is the value of 9a + 8b?

Learn how to solve the algebraic equation 3/4a + 2/3b = 7 to find the value of 9a + 8b. This problem covers key algebraic concepts such as fraction manipulation and linear equations. Suitable for students in Grades 8-10.

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