Two numbers are in the ratio $$ 8: 5 $$. If the larger number is 56 , find the smaller number. Two numbers are in the ratio $$ 9: 8 $$. If the smaller number is 128 , find the larger number. Four diaries cost R 500 . How much will thirteen diaries cost? Nine pens cost R504. How many pens will cost R4 032? If one pack of 100 masks costs R90, how much will you pay for 80 packs? If 260 grams of flour is needed to bake 13 muffins, how many grams of flour will be needed to bake 10 muffins?

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Sure, let's solve each problem step by step.

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**1. Two numbers are in the ratio $$ 8:5 $$. If the larger number is 56, find the smaller number.**

**Solution:**

Given the ratio of two numbers is $$ 8:5 $$, where 8 corresponds to the larger number.

Let the two numbers be $$ 8k $$ and $$ 5k $$.

Given that the larger number $$ 8k = 56 $$.

Solve for $$ k $$:
$$
k = \frac{56}{8} = 7
$$

Now, find the smaller number:
$$
5k = 5 \times 7 = 35
$$

**Answer:** The smaller number is **35**.

---

**2. Two numbers are in the ratio $$ 9:8 $$. If the smaller number is 128, find the larger number.**

**Solution:**

Let the two numbers be $$ 9k $$ (larger) and $$ 8k $$ (smaller).

Given $$ 8k = 128 $$.

Solve for $$ k $$:
$$
k = \frac{128}{8} = 16
$$

Now, find the larger number:
$$
9k = 9 \times 16 = 144
$$

**Answer:** The larger number is **144**.

---

**3. Four diaries cost R500. How much will thirteen diaries cost?**

**Solution:**

First, find the cost per diary:
$$
\text{Cost per diary} = \frac{500}{4} = R125 \text{ per diary}
$$

Now, find the cost for thirteen diaries:
$$
13 \times 125 = R1,625
$$

**Answer:** Thirteen diaries will cost **R1,625**.

---

**4. Nine pens cost R504. How many pens will cost R4,032?**

**Solution:**

First, find the cost per pen:
$$
\text{Cost per pen} = \frac{504}{9} = R56 \text{ per pen}
$$

Now, find the number of pens that cost R4,032:
$$
\frac{4,032}{56} = 72 \text{ pens}
$$

**Answer:** R4,032 will buy **72 pens**.

---

**5. If one pack of 100 masks costs R90, how much will you pay for 80 packs?**

**Solution:**

First, find the cost per pack:
$$
\text{Cost per pack} = R90
$$

Now, find the cost for 80 packs:
$$
80 \times 90 = R7,200
$$

**Answer:** 80 packs will cost **R7,200**.

---

**6. If 260 grams of flour is needed to bake 13 muffins, how many grams of flour will be needed to bake 10 muffins?**

**Solution:**

First, find the amount of flour per muffin:
$$
\text{Flour per muffin} = \frac{260}{13} = 20 \text{ grams per muffin}
$$

Now, find the amount needed for 10 muffins:
$$
10 \times 20 = 200 \text{ grams}
$$

**Answer:** You will need **200 grams** of flour to bake 10 muffins.

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If you have any further questions or need more explanations, feel free to ask!
1. The smaller number is **35**. 2. The larger number is **144**. 3. Thirteen diaries will cost **R1,625**. 4. R4,032 will buy **72 pens**. 5. 80 packs will cost **R7,200**. 6. You will need **200 grams** of flour to bake 10 muffins.

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