Question

Anthony's age plus the cube of Collin's age is 1,739. Collin's age plus the cube of

Anthony's age is 1,343. How old are Collin and Anthony?

Answer 1

Collin is approximately 10 years old and Anthony is approximately 739 years old

Explanation:

Let's assume Anthony's age is represented by 'A' and Collin's age is represented by 'C'.

According to the given information, we have two equations:

A + C^3 = 1,739

C + A^3 = 1,343

We can solve these equations simultaneously to find the values of A and C.

From equation 1, we have: A = 1,739 - C^3

Substituting this value of A into equation 2, we get:

C + (1,739 - C^3)^3 = 1,343

Expanding and simplifying the equation, we can solve for C.

After solving the equation, we find that Collin's age (C) is approximately 10.

Substituting this value of C back into equation 1, we can find Anthony's age (A):

A + 10^3 = 1,739

A + 1000 = 1,739

A = 1,739 - 1000

A = 739

Therefore, Collin is approximately 10 years old and Anthony is approximately 739 years old.

Answer 2

Collin is 12 years old.

Anthony is 11 years old.

Explanation:

To find the age of Collin and Anthony, we can use the strategy of "Guess and Check".

We are told that Anthony's age plus the cube of Collin's age is 1,739.

If we let "A" be Anthony's age and "C" be Collins age then the equation that models this information is:

`A + C^3=1739`

Rearrange the equation to isolate Anthony's age (A):

`A=1739-C^3`

As the cube of 10 is 1000, we can immediately conclude that Collin must be older than 10 years old, as if Collin was 10 years old, then Anthony would be 739 years old (which is unrealistic!).

Let's try assuming Collin is 11 years old.

Substituting C = 11 into the equation gives:

`A=1739-11^3=408`

Again, we can conclude that Collin must be older that 11 years old, since this would make Anthony the unrealistic age of 408 years old!

Let's try assuming Collin is 12 years old.

Substituting C = 12 into the equation gives:

`A=1739-12^3=11`

We now have a very realistic age for Anthony, so Collin could be 12 years old and Anthony could be 11 years old.

The second piece of given information tells us that Collin's age plus the cube of Anthony's age is 1,343. In equation form, this is:

`C+A^3=1343`

Substitute the possible ages for Collin (C = 12) and Anthony (A = 11) into this second equation:

`\begin{aligned}12 + 11^3 &=12 + 1331 \\&= 1343\end{aligned}`

As this equation holds true, this confirms that:

• Collin is 12 years old.
• Anthony is 11 years old.