Question

The sum of three numbers is 143. The third number is 3 times the second. The first number is 7 less than the second. What are the numbers?"

Answer 1

The three numbers that satisfy the conditions of the sum being 143, the third being three times the second, and the first being seven less than the second, are 23, 30, and 90.

Step-by-step explanation:

The question involves solving a system of linear equations to find three numbers that satisfy given conditions. Let's denote the second number as s, the third number as t, and the first number as f. From the problem, we have the following equations:

• f + s + t = 143
• t = 3s
• f = s - 7

To solve these equations, begin by substituting the expressions for t and f into the first equation:

1. s - 7 + s + 3s = 143
2. 5s - 7 = 143
3. 5s = 150
4. s = 30

Now that we have the value of s, we can find f and t:

• f = s - 7 = 30 - 7 = 23
• t = 3s = 3 × 30 = 90

Therefore, the three numbers are 23, 30, and 90.