One half of the sum of three consecutive multiples of 10 is 90. What are the multiples of 10?
first represent the unknowns using variables.
let x = first multiple of 10
since consecutive multiples of ten has difference of 10 (example 40 and 30 has a difference of 10),
let x + 10 = second multiple of 10
let x + 20 = third multiple of 10
then we set-up the equation. from the first statement of the problem,
(1/2)*(x + x + 10 + x + 20) = 90
then we solve for x:
(1/2)*(3x + 30) = 90
3x + 30 = 180
3x = 150
x = 50 (first multiple)
x + 10 = 60 (second multiple
x + 20 = 70 (third multiple)
hope this helps~ :)
To solve this problem, we need to find three consecutive multiples of 10 that satisfy the given condition.
Let's assume the first multiple of 10 is represented by the variable 'x'.
Therefore, the second multiple of 10 would be 'x + 10' and the third multiple of 10 would be 'x + 20'.
According to the problem, one half of the sum of these three consecutive multiples of 10 is 90. So, we can set up the following equation:
(1/2)(x + (x + 10) + (x + 20)) = 90
Now, let's solve this equation step by step to find the value of 'x':
First, simplify each term within the parentheses:
(1/2)(3x + 30) = 90
Next, remove the parentheses by multiplying each term by (1/2):
(3x + 30)/2 = 90
Multiply both sides of the equation by 2 to eliminate the fraction:
3x + 30 = 180
Subtract 30 from both sides:
3x = 150
Divide both sides by 3 to isolate the variable 'x':
x = 50
So, the first multiple of 10 is 50, the second multiple is 50 + 10 = 60, and the third multiple is 50 + 20 = 70.
Therefore, the multiples of 10 are: 50, 60, and 70.