The sum of two numbers is 21 and one number is twice the other. What are the numbers?

Question

UpStudy AI · Accepted Answer

Let's solve the problem step by step.

**Problem Statement:**
- The sum of two numbers is 21.
- One number is twice the other.

**Let's define the variables:**
- Let $$ x $$ be the first number.
- Let $$ y $$ be the second number.

**According to the problem:**
1. $$ x + y = 21 $$  *(The sum of the two numbers is 21.)*
2. $$ y = 2x $$    *(One number is twice the other.)*

**Now, substitute equation (2) into equation (1):**
$$
x + (2x) = 21
$$
$$
3x = 21
$$
$$
x = \frac{21}{3} = 7
$$

**Now, find $$ y $$ using equation (2):**
$$
y = 2x = 2 \times 7 = 14
$$

**Solution:**
- The first number is **7**.
- The second number is **14**.

**Verification:**
- Sum: $$ 7 + 14 = 21 $$ ✅
- One number is twice the other: $$ 14 = 2 \times 7 $$ ✅

Both conditions are satisfied.
The numbers are 7 and 14.

Solución de inteligencia artificial de Upstudy