Test Prep 5 Shia has 6 new boxes of crayons. Each box has 8 crayons. He also has 7 crayons from an old box. How many crayons does he have? (A) 21 (B) 42 (C) 48 (D) 55 6 Kira has 3 shelves of books. Each shelf has 4 books. She also has 5 books that are not on shelves. How many books does she have? Write two equations with letters for the unknowns. Solve. - 7 Vera cut a piece of fabric into 5 equal-length pieces. Then she cut another 3 centimeters off one piece, leaving 6 centimeters of fabric. How many centimeters long was her original piece of fabric? Write two equations with letters for the unknowns. Solve. (

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Sure, let's tackle each of these problems step by step.

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### **Problem 5**

**Shia has 6 new boxes of crayons. Each box has 8 crayons. He also has 7 crayons from an old box. How many crayons does he have?**

**Answer Choices:**
- (A) 21
- (B) 42
- (C) 48
- (D) 55

**Solution:**

1. **Calculate the number of crayons in the new boxes:**
   - **Number of new boxes:** 6
   - **Crayons per box:** 8
   - **Total crayons from new boxes:** $$ 6 \times 8 = 48 $$

2. **Add the crayons from the old box:**
   - **Crayons from the old box:** 7
   - **Total crayons:** $$ 48 + 7 = 55 $$

**Answer:** (D) 55

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### **Problem 6**

**Kira has 3 shelves of books. Each shelf has 4 books. She also has 5 books that are not on shelves. How many books does she have? Write two equations with letters for the unknowns. Solve.**

**Solution:**

Let's define the variables:

- Let $$ s $$ = number of shelves
- Let $$ b $$ = number of books per shelf
- Let $$ o $$ = number of books not on shelves
- Let $$ T $$ = Total number of books

**Equations:**

1. **Total books on shelves:**
   $$
   \text{Books on shelves} = s \times b
   $$
   
2. **Total books including those not on shelves:**
   $$
   T = (s \times b) + o
   $$

**Given Values:**

- $$ s = 3 $$ shelves
- $$ b = 4 $$ books per shelf
- $$ o = 5 $$ books not on shelves

**Plugging in the values:**

1. **Books on shelves:**
   $$
   \text{Books on shelves} = 3 \times 4 = 12
   $$
   
2. **Total books:**
   $$
   T = 12 + 5 = 17
   $$

**Answer:** Kira has **17 books** in total.

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### **Problem 7**

**Vera cut a piece of fabric into 5 equal-length pieces. Then she cut another 3 centimeters off one piece, leaving 6 centimeters of fabric. How many centimeters long was her original piece of fabric? Write two equations with letters for the unknowns. Solve.**

**Solution:**

Let's define the variables:

- Let $$ L $$ = original length of the fabric (in centimeters)
- Let $$ x $$ = length of each equal-length piece before cutting off

**Equations:**

1. **Total length divided into equal pieces:**
   $$
   L = 5x
   $$
   
2. **After cutting off 3 cm from one piece, that piece is 6 cm:**
   $$
   x - 3 = 6
   $$

**Solving the Equations:**

1. **From the second equation:**
   $$
   x - 3 = 6 \
   x = 6 + 3 \
   x = 9 \text{ cm}
   $$
   
2. **Substitute $$ x $$ into the first equation:**
   $$
   L = 5x = 5 \times 9 = 45 \text{ cm}
   $$

**Answer:** Vera's original piece of fabric was **45 centimeters** long.

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If you have any more questions or need further clarification on these problems, feel free to ask!
**Problem 5:** Shia has 6 boxes with 8 crayons each and 7 from an old box. Total crayons: 6 × 8 + 7 = 55. **Answer:** (D) 55 **Problem 6:** Kira has 3 shelves with 4 books each and 5 books not on shelves. Total books: (3 × 4) + 5 = 17. **Answer:** 17 books **Problem 7:** Vera cuts a fabric into 5 equal pieces, then cuts 3 cm from one piece, leaving 6 cm. Original length: 5 × (6 + 3) = 45 cm. **Answer:** 45 centimeters

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