1. If the product of 5 and the sum of 10 and a certain number is equal to 15, what is the number? 2. The sum of two consecutive counting numbers divided by their positive difference is 9. Find the larger numbers.
5(10 + n) = 15
50 + 5n = 15
5n = -35
n = ?
n=35/5
7
sorry wrong solution
5n=-35
n=-35/5
n=-7
5×10+x=15
(5×10=50)
50+x=15
Collect like terms
X=15-50=-35
So therefore x=35
Sorry I MEANT X=-35
1. Well, let's break it down. The product of 5 and the sum of 10 and a certain number is equal to 15. So we have 5 * (10 + x) = 15. Now, let's simplify it: 50 + 5x = 15. Subtracting 50 from both sides, we get 5x = -35. Divide both sides by 5, and we find that x = -7. So, the certain number is -7. But hey, cheer up, at least it's not a positive clown!
2. Ah, the joys of consecutive counting numbers. Let's call the smaller number x and the larger number x+1. We're told that their sum divided by their positive difference is 9. So, (x + (x + 1)) / ((x + 1) - x) = 9. Simplifying a bit, we get (2x + 1) / 1 = 9. Ah-ha! Now it's clear. 2x + 1 = 9. Subtracting 1 from both sides, we find that 2x = 8. Dividing both sides by 2, we get x = 4. So, the larger number is 5. Voila!
1. To solve this problem, we can follow these steps:
Step 1: Let's assume the unknown number as x.
Step 2: According to the problem, the product of 5 and the sum of 10 and the unknown number (x) is equal to 15. This can be written as:
5 * (10 + x) = 15
Step 3: Simplify the equation:
50 + 5x = 15
Step 4: Subtract 50 from both sides of the equation:
5x = 15 - 50
5x = -35
Step 5: Divide both sides of the equation by 5:
x = -35/5
x = -7
So, the number is -7.
2. Let's follow these steps to solve this problem:
Step 1: Let's assume the smaller consecutive counting number as x, and the larger consecutive counting number as x + 1.
Step 2: According to the problem, the sum of the two consecutive counting numbers divided by their positive difference is equal to 9. This can be written as:
(x + x + 1) / (x + 1 - x) = 9
Step 3: Simplify the equation:
(2x + 1) / 1 = 9
2x + 1 = 9
Step 4: Subtract 1 from both sides of the equation:
2x = 9 - 1
2x = 8
Step 5: Divide both sides of the equation by 2:
x = 8/2
x = 4
Step 6: Find the larger number by adding 1 to the smaller number:
x + 1 = 4 + 1
x + 1 = 5
So, the larger numbers are 4 and 5.