Question

Mack is double Cici's age. Three times Mack's age minus two times Cici's age is 52. How old is Mack

Answer 1

$\underline{\large\text{Part I: Converting the statements into equations or expressions.}}$

Given statements:

• Mack is double Cici's age.
• Three times Mack's age minus two times Cici's age is 52.

First statement:

We know the following:

• The word "double" means 2 times greater than a number or variable.
• The word "is" means "=", which states that two expressions or terms are equivalent.

Therefore, the first statement, when converted into an equation, is;

• ⇒ Mack = 2(Cici)

Let Mack be known as "M" and Cici be known as "C". Then,

• ⇒ M = 2C

Second statement:

We know the following:

• The phrase "three times" means "triple", which means 3 times greater than the original number.
• The phrase "two times" means "double", which means 2 times greater than the original number.
• The word "is" means "equivalent".

Therefore, the second statement, when converted into an equation, is;

• ⇒ 3(Mack) + 2(Cici) = 52

Let Mack be known as "M" and Cici be known as "C". Then,

• ⇒ 3(M) + 2(C) = 52

$\underline{\large\text{Part II: Using the equations obtained to determine the age of Mack}}$

From the above, we obtained:

• Equation 1: M = 2C
• Equation 2: 3(M) + 2(C) = 52

When the value of "M", in equation 1, is substituted in equation 2, we get;

• ⇒ 3(2C) + 2(C) = 52   [M = 2C]

When simplified, we get;

• ⇒ 3(2C) + 2(C) = 52
• ⇒ 6C + 2C = 52          
• ⇒ 8C = 52      
• ⇒ 8C/8 = 52/8
• ⇒ C = 52/8 = 26/4 = 13/2 = 6.5

Therefore, the age of Cici is 6.5 years.

But, we are asked to determine the age of Mack. Simply substitute the age of Cici in equation 1 to determine the age of Mack.

• ⇒ M = 2C
• ⇒ M = 2(6.5)
• ⇒ M = 13

Therefore, the age of Mack is 13 years.

Learn more about this topic: brainly.com/question/26032086