[tex]\underline{\large\text{Part I: Converting the statements into equations or expressions.}}[/tex]
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;
Let Mack be known as "M" and Cici be known as "C". Then,
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;
Let Mack be known as "M" and Cici be known as "C". Then,
[tex]\underline{\large\text{Part II: Using the equations obtained to determine the age of Mack}}[/tex]
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.
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