Write the equation and solve the following problems
1. Seven more then three times a number is 22. What is the number?
2. One half a number diminished by six is 14. What is the number?
3. The sum of two consecutive numbers is 131. What are the numbers.
4. One number is 5 more than the other. Three times the smaller is equal to twice the larger. What are the two numbers?
1.
3n + 7 = 22
3.
x + x + 1 = 131
I'll be glad to check your answers to the other two problems.
Sure! Let's solve each problem step by step:
1. Seven more than three times a number is 22. Let's call the number "x". The equation representing this problem is:
3x + 7 = 22
To solve the equation, we need to isolate the variable "x". First, we subtract 7 from both sides:
3x = 22 - 7
3x = 15
Then, we divide both sides by 3:
x = 15 / 3
x = 5
So the number is 5.
2. One-half a number diminished by six is 14. Let's call the number "x" again. The equation representing this problem is:
(1/2)x - 6 = 14
To solve the equation, we first get rid of the fraction by multiplying both sides by 2:
2 * ((1/2)x - 6) = 2 * 14
x - 12 = 28
Next, we add 12 to both sides:
x = 28 + 12
x = 40
So the number is 40.
3. The sum of two consecutive numbers is 131. Let's call the first number "x". The equation representing this problem is:
x + (x + 1) = 131
To solve the equation, we combine like terms:
2x + 1 = 131
Next, we subtract 1 from both sides:
2x = 131 - 1
2x = 130
Then, we divide both sides by 2:
x = 130 / 2
x = 65
So the two consecutive numbers are 65 and 66.
4. One number is 5 more than the other. Three times the smaller is equal to twice the larger. Let's call the smaller number "x" and the larger number "y". The equation representing this problem is:
x = y - 5
3x = 2y
To solve the equation, we need to substitute the value of x in the second equation. Substituting y - 5 for x, we get:
3(y - 5) = 2y
Expanding and simplifying:
3y - 15 = 2y
Next, we subtract 2y from both sides:
y - 15 = 0
Finally, we add 15 to both sides:
y = 15
Substituting y = 15 into the first equation, we can find the value of x:
x = 15 - 5
x = 10
So the two numbers are 10 and 15.