Two times becky's age plus three times sara's age is 165. Becky's age is one-third of Sara's age. How old is sara?

To solve this problem, you have to work backwards. We can write this as an equation to solve it. We can use the letter "b" to represent Becky's age while "s" can be used for Sara's age.

2b+3s=165

We have to keep in mind that Becky's age is ⅓ of Sara's age, so we could also add on to this equation.

2b+3s=165 and b=⅓s

Since we know that b=⅓ and that Becky's age times two is used in the equation, we can multiply both sides by 2.

(2)b=(2)⅓s

2b=⅔s

Since we know that 2b=⅔s, we can add that to the 3s in the equation.

⅔s+3s=3⅔s

So, now the equation is:

3⅔s=165

To make it a bit easier for us, we can convert 3⅔ into an improper fraction.

3⅔=¹¹⁄₃

Now, we can start solving the problem. Since 11 is being divided by 3, we can do the opposite operation and multiply both sides by 3.

[¹¹⁄₃(3)]s=165(3)

11s=495

Now, we can divide both sides by 11 to get the value of s.

11s÷11=495÷11

s=45

So, Sara's age is 45.

Check:

Since we know that Becky's age is ⅓ of Sara's age, we can divide 45 by 3 to get Becky's age.

45÷3=15

Now we know that Becky's age is 15. Since the equation is 2b+3s=165, we can multiply 15 by 2 and 45 by 3.

15×2=30

45×3=135

Now, we can simplify the equation.

30+135=165

165=165

So, the answer is correct.