The average of five numbers is 18. let the first number be increased by 1, the second number by 2, the third number by 3, the fourth number by 4, and the fifth number by 5. what is the average of the set of increased numbers?

21

Step-by-step explanation:

Let x, y, z, t, u represent the five numbers. Since their average is 18,

(x + y + z + t + u) / 5 = 18  

→ x + y + z + t + u = 90  (1)

If the first number is increased by 1, the second number by 2, the third number by 3, the fourth number by 4, and the fifth number by 5, then the total of the numbers will be

(x+1) + (y+2) + (z+3) + (t+4) + (u+5)

→ x + y + z + t + u + 15   (Substitute x + y + z + t + u from equation 1)

→ 90 + 15 = 105

If the total of increased numbers is 105, then the average is

105 / 5 = 21

nothjing

step-by-step explanation:

simplifying

5(x + -6) = 2(x + 3)

reorder the terms:

5(-6 + x) = 2(x + 3)

(-6 * 5 + x * 5) = 2(x + 3)

(-30 + 5x) = 2(x + 3)

reorder the terms:

-30 + 5x = 2(3 + x)

-30 + 5x = (3 * 2 + x * 2)

-30 + 5x = (6 + 2x)

solving

-30 + 5x = 6 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-30 + 5x + -2x = 6 + 2x + -2x

combine like terms: 5x + -2x = 3x

-30 + 3x = 6 + 2x + -2x

combine like terms: 2x + -2x = 0

-30 + 3x = 6 + 0

-30 + 3x = 6

add '30' to each side of the equation.

-30 + 30 + 3x = 6 + 30

combine like terms: -30 + 30 = 0

0 + 3x = 6 + 30

3x = 6 + 30

combine like terms: 6 + 30 = 36

3x = 36

divide each side by '3'.

x = 12

simplifying

x = 12

this should .