Let's break down and solve the problems presented in the image:

Problem 22:

$\frac{2}{3}q + 2 = 1q$

Solution:

1. Rearrange the equation to isolate $q$: $\frac{2}{3}q - 1q = -2$ This simplifies to: $\left(\frac{2}{3} - 1\right)q = -2$ $-\frac{1}{3}q = -2$
2. Solve for $q$: $q = -2 \times -3 = 6$

So, the value of $q = 6$.

Problem 23:

$\frac{7}{8}a = 5a - 6$

Solution:

1. Rearrange the equation: $\frac{7}{8}a - 5a = -6$ To simplify, find a common denominator: $\frac{7}{8}a - \frac{40}{8}a = -6$ $\frac{-33}{8}a = -6$
2. Solve for $a$: $a = \frac{-6 \times 8}{-33}$ $a = \frac{48}{33} = \frac{16}{11}$

So, $a = \frac{16}{11}$.

Problem 24: Fill in the blanks for conversions

(a) $1 \, \text{liter} = \, \_\_ \, \text{ml}$

$1 \, \text{liter} = 1000 \, \text{ml}$

(b) $1 \, \text{pt} = \, \_\_ \, \text{c}$

$1 \, \text{pt} = 2 \, \text{c}$

(c) $1 \, \text{gal} = \, \_\_ \, \text{qt}$

$1 \, \text{gal} = 4 \, \text{qt}$

Problem 25: Stamp Collector Problem

Question: A stamp collector has 5,460 stamps. 1,428 of them are from the United States. 1,376 of them are from Europe. The rest are from Asia. How many stamps from Asia does the stamp collector have?

Solution:

1. Total stamps = 5,460
2. Stamps from the United States = 1,428
3. Stamps from Europe = 1,376

Stamps from Asia: $5,460 - (1,428 + 1,376) = 5,460 - 2,804 = 2,656$

So, the collector has 2,656 stamps from Asia.

Would you like more details on any of the steps or additional explanation?

5 Related Questions:

1. How can you check if the solution for a linear equation is correct?
2. What other methods can you use to solve a linear equation?
3. How are conversions between units like liters and milliliters handled mathematically?
4. Can you generalize the steps for solving equations involving fractions?
5. How would the result change in the stamp collector problem if there were more regions?

Tip:

When solving equations involving fractions, always clear the fractions early by multiplying through by the least common denominator (LCD) to simplify the problem!