Four times the sum of a number and 3 is the same as the sum of two times the number and 8. Find the number.

Step-by-step explanation:

4 (x + 3) = 2x + 8   <"four times the sum of a number and three is equal to eight more than twice the number."

Second, we want to solve the equation:

4 (x + 3) = 2x + 8

4x + 12 = 2x + 8

2x + 12 = 8       <subtract 2x from both sides of the equation.

2x = -4              <subtract -12 from both sides

x = -2                <divide both sides by 2 which leaves a negative answer

Third, we want to check the answer by substituting the value of -2 for x in the original equation.

4 (x + 3) = 2x + 8

4 (-2 +3) = 2(-2) + 8

-8 + 12 = -4 + 8

  4        =      4

4 (x + 3) = 2x + 8   <"four times the sum of a number and three is equal to eight more than twice the number."

Second, we want to solve the equation:

4 (x + 3) = 2x + 8

4x + 12 = 2x + 8

2x + 12 = 8       <subtract 2x from both sides of the equation.

2x = -4              <subtract -12 from both sides

x = -2                <divide both sides by 2 which leaves a negative answer

Third, we want to check the answer by substituting the value of -2 for x in the original equation.

4 (x + 3) = 2x + 8

4 (-2 +3) = 2(-2) + 8

-8 + 12 = -4 + 8

  4        =      4

constant of proportionality = 3 and the equation is c = 3p.

step-by-step explanation:

c = kp   where c = amount of caffeine in mg., p = oz of pepsi and k is the constant of proportionality.

substituting the values given:

24 = 8k

k = 3.

the same value of k will be obtained if we substitute the other given values.