7. The sum of seven consecutive integers is 175. What is the difference between twice the largest number and thrice the smallest number?
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7. The sum of seven consecutive integers is 175. What is the difference between twice the largest number and thrice the smallest number?
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Answer:
-10
Step-by-step explanation:
From the problem, we know that the sum of seven consecutive numbers is 175. We are asked to determine the difference between twice the largest number and thrice the smallest number. For this, we can let
be the smallest number. The numbers succeeding this number will then be
x + 1,x + 2,x + 3,x +4,x + 5,x + 6,x
in increasing order. We will first set up the equation for the scenario stated in the problem and solve for the value of x
. This will help us determine what the smallest and largest numbers are.
Answer:
To solve this problem, let's break it down into steps.
Step 1: Let's represent the consecutive integers. To find their sum, we'll use the concept of an arithmetic series. We'll let the smallest integer be 'x', then the next integers will be 'x + 1', 'x + 2', 'x + 3', 'x + 4', 'x + 5', and 'x + 6'.
Step 2: Formulate the equation for the sum of the consecutive integers. The sum is given as 175, so we can write:
x + (x + 1) + (x + 2) + (x + 3) + (x + 4) + (x + 5) + (x + 6) = 175
Step 3: Simplify the equation by combining like terms:
7x + 21 = 175
Step 4: Solve the equation for 'x':
7x = 175 - 21
7x = 154
x = 154 / 7
x = 22
Step 5: Find the largest and smallest numbers by substituting 'x' into the consecutive integer expressions.
The smallest number is x = 22, and the largest number is x + 6 = 22 + 6 = 28
Step 6: Calculate the difference between twice the largest number and thrice the smallest number:
2 * 28 - 3 * 22 = 56 - 66 = -10
Therefore, the difference between twice the largest number and thrice the smallest number is -10.
Step-by-step explanation:
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