Mrs. Smith is 2 years more than 3 times as old as her son. If the difference between their ages is 22 years,?

Question

Mrs. Smith is 2 years more than 3 times as old as her son. If the difference between their ages is 22 years, how old is Mrs. Smith?

Answer 1

(3x+2) - (x) = 22

2x+2 = 22

2x = 20

x=10 ----The son is 10


So for the mom-

3x+2 = 3(10)+2 = 30 + 2 = 32

Answer 2

You need to think in terms of "x". The son's age is an unknown, so we will call it "x". Mrs. Smith's age is also unknown. But we do know she is 2 years more than 3 times the son's age. So if the son is x years old, Mrs. Smith is 3x +2 years old (3 times x, plus two years). We also know the difference in age is 22. Whenever you see the word "difference", you should know it's a subtraction problem. So the difference between the two ages is expressed as (3x + 2) - x = 22. In other words, Mrs. Smith's age minus the son's age is 22. Now just combine like terms and solve for x. Once you know x, you also can figure out Mrs. Smith's age by plugging in the value for x into 3x +2. Good luck!

Answer 3

This is a really easy problem, you just need to know how to set it up. Let us use a variable 'M' to represent Mrs. Smith, and 'S' to represent her son. Now we simply write the two formulas using mathematical notations:

M = 2 + 3 x S
M - S = 22
Note: We know by inference that the parent is always older than the child, so to get a positive "22", we will subtract the son's age from the parent.

Now we simply substitue the isolated 'M' (we could isolate 'S' and do it that way to), into one of the equations. So, we get:
(2 + 3 x S) - S = 22
Follow the simple steps of reducing 'S':
2 + 2 x S = 22
Subtract 2 from both sides:
2 x S = 20
After dividing both sides by 2, you get:
S = 20
Now just go back to the original equations:
M = 2 + 3* S
and you will have your answer.


Once you understand what is going on here, you'll be able to do these problems without much thought. It's just following the same patern. Sometimes, you will need to isolate a variable so as to make the substitution. You might also want to know that for each "unknown", there will be another relationship. That is to say, if there are 3 unknowns, there will be three relationships. In this case there are two unknowns and two relationships.

Good Luck.

Answer 4

Mrs. Smith is 32 and her son is 10.
Use the equation 3x+2-x=22 set equal to zero
3x+2-x-22=0 and solve for x
Check your answer

Answer 5

I just used my head... I started at 7x3, then 8x3, until I got to 10.

At 10 yrs old x 3 = 30
+2 = 32

and 32 is 22 more than 10. I do everything in my head, is that bad? I hate Algebra, but love Geometry. I also answer questions like what's 549 x 55 rather closely or right on, because I make it 500x50, then 50x5 and add the result together and remove the extra, or give an approximate answer if that's what is desired.

thanks for the math fun!

Answer 6

ok, designate your givens:

let 'x' represent Mrs. Smith's son
since Mrs Smith is 3 times her son plus 2 years, let '3x+2' represent Mrs Smith

difference means subtraction, therefore your equation should look like this:
(Mrs. Smith) - (Mrs Smiths son) = 22
(3x+2) - (x) = 22
combine like terms (3x+2-x)... 2x+2 = 22, get x alone by subtracting 2 from both sides...2x=20, divide both sides by 2...therefore x=10...substitute back into the original equations for each individual and you have:

(3x+2)...(3*10+2)--order of operations--mrs smith is 32
and her son is 10

Answer 7

Mrs. Smith is 32, and her son is 10

Answer 8

MRS. SMITH IS 32 AND HER SON IS 10.

Answer 9

x=sons age
so 3x+2 equals mom's age
so 3x+2-x = 22
2x+2=22
2x=20
10=x

Answer 10

10 and 32.