Question

① use substitution to match these solutions to their equations. {15, 12, 9, 63}
$\frac{a}{9} - 4 = 3$, $a =$ ______
$6b - 18 = 36$, $b =$ ______
$\frac{1}{3}c + 2 = 7$, $c =$ ______
② which expression is equal to: $12b + 3a$
a $(a + b) \cdot 12$ b $3(4b + a)$
c $ab \cdot 12 \cdot 3$ d $(12 \cdot 3) + (b \cdot a)$
③ $ spent on apps per month:
16, 12, 18, 17, 16, 8, 7, 2
mean = ____ median = ____
mode(s) = ____ range = ____
④ use the data from the frequency table to complete the histogram.
⑤ how many cats are in the shelter?

weight	frequency
6 - 10	12
11 - 15	6
16 - 20	1

weights of cats in the shelter
(frequency axis: 0,2,4,6,8,10,12; pounds axis: 1 - 5, 6 - 10, 11 - 15, 16 - 20)

Explanation:

Step1: Solve for $a$

Start with $\frac{a}{9} - 4 = 3$. Add 4 to both sides:
$\frac{a}{9} = 3 + 4 = 7$
Multiply by 9: $a = 7 \times 9 = 63$

Step2: Solve for $b$

Start with $6b - 18 = 36$. Add 18 to both sides:
$6b = 36 + 18 = 54$
Divide by 6: $b = \frac{54}{6} = 9$

Step3: Solve for $c$

Start with $\frac{1}{3}c + 2 = 7$. Subtract 2 from both sides:
$\frac{1}{3}c = 7 - 2 = 5$
Multiply by 3: $c = 5 \times 3 = 15$

Step4: Match equivalent expression

Factor $12b + 3a$: factor out 3:
$3(4b + a)$
Compare to options: matches option B.

Step5: Calculate mean (app spending)

Sum all values: $16 + 12 + 18 + 17 + 16 + 8 + 7 + 2 = 96$
Divide by count (8): $\text{mean} = \frac{96}{8} = 12$

Step6: Calculate median (app spending)

Order values: $2, 7, 8, 12, 16, 16, 17, 18$
Average 4th/5th terms: $\text{median} = \frac{12 + 16}{2} = 14$

Step7: Find mode (app spending)

Identify most frequent value: 16 appears twice, others once. $\text{mode} = 16$

Step8: Calculate range (app spending)

Subtract min from max: $\text{range} = 18 - 2 = 16$

Step9: Count total cats

Sum frequencies: $3 + 12 + 6 + 1 = 22$

Step10: Prepare histogram data

For each weight group:

• 1-5: frequency = 3
• 6-10: frequency = 12
• 11-15: frequency = 6
• 16-20: frequency = 1

Draw bars to match these heights on the histogram axes.

Answer:

1. $a = 63$, $b = 9$, $c = 15$
2. B. $3(4b + a)$
3. $\text{mean} = 12$, $\text{median} = 14$, $\text{mode(s)} = 16$, $\text{range} = 16$
4. Histogram: Draw a bar of height 3 for 1-5, height 12 for 6-10, height 6 for 11-15, height 1 for 16-20
5. 22