Three-eighths of a number, decreased
by 1 , is 5 . Find the number.
Seven diminished by of a number

Question

Three-eighths of a number, decreased by 1 , is 5 . Find the number. Seven diminished by $$ \frac{1}{4} $$ of a number

UpStudy AI · Accepted Answer

Let's tackle both problems step by step.

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### **1. Three-eighths of a Number, Decreased by 1, is 5**

**Problem Statement:**
"Three-eighths of a number, decreased by 1, is 5. Find the number."

**Let’s denote the unknown number as $$ x $$.**

**Step-by-Step Solution:**

1. **Translate the problem into an equation:**

$$
   \frac{3}{8}x - 1 = 5
   $$

2. **Add 1 to both sides to isolate the term with $$ x $$:**

$$
   \frac{3}{8}x = 5 + 1 \
   \frac{3}{8}x = 6
   $$

3. **Multiply both sides by the reciprocal of $$ \frac{3}{8} $$ to solve for $$ x $$:**

$$
   x = 6 \times \frac{8}{3} \
   x = \frac{48}{3} \
   x = 16
   $$

**Answer:** The number is **16**.

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### **2. Seven Diminished by $$ \frac{1}{4} $$ of a Number**

**Problem Statement:**
"Seven diminished by $$ \frac{1}{4} $$ of a number."

**Interpretation:**
To "diminish" means to subtract. So, "seven diminished by $$ \frac{1}{4} $$ of a number" translates to:

$$
7 - \frac{1}{4}x
$$

**Explanation:**

- **"Seven"** is the starting value.
- **"Diminished by $$ \frac{1}{4} $$ of a number"** means you subtract $$ \frac{1}{4}x $$ from seven.

**Final Expression:**

$$
7 - \frac{1}{4}x
$$

**Note:** If there's additional information or if you need to solve for $$ x $$ based on this expression equating to a specific value, please provide that detail!

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The number is 16.

Three-eighths of a number, decreased
by 1 , is 5 . Find the number.
Seven diminished by of a number

Upstudy AI Solution

Answer

Solution

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Three-eighths of a number, decreased by 1 , is 5 . Find the number. Seven diminished by of a number

Upstudy AI Solution

Answer

Solution

Extra Insights

Related Questions

Latest Algebra Questions

Three-eighths of a number, decreased
by 1 , is 5 . Find the number.
Seven diminished by of a number