Question 1163625: Gracie is four years younger than Rose💚Gracie is four years younger than Rose. The sum of their ages is 24. What are their ages?
Found 3 solutions by Theo, MathTherapy, greenestamps:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! g = gracie's age
r = rose's age
g = r - 4
g + r = 24
replace g in the first eqaution with r - 4 to get:
r - 4 + r = 24
combine like terms to get:
2r - 4 = 24
add 4 to both sides of the equation to get:
2r = 28
solve for r to get:
r = 28/2 = 14
since g = r - 4, then you get:
r = 14
g = 10
that's their ages.
rosie is 14.
gracie is 10.
Answer by MathTherapy(10552)  (Show Source):
You can put this solution on YOUR website! Gracie is four years younger than Rose💚Gracie is four years younger than Rose. The sum of their ages is 24. What are their ages?
Let Gracie's and Rose's ages be G and R
We then get: R - G = 4 ----- eq (i)
Also, R + G = 24 ------ eq (ii)
Add the 2 equations and simplify to find R, Rose's age.
Use that value in eq (ii) to find G, or Gracie's age!
Answer by greenestamps(13200)  (Show Source):
You can put this solution on YOUR website!
You have two responses showing different formal algebraic methods for solving the problem.
The problem is one of a large number of very different problems which reduce to the same thing: the sum of two numbers is some number, and their difference is some other number. In this case, the sum is 24 and the difference is 4.
Here is a quick and easy informal method for solving any problem like this (if, of course, a formal algebraic solution is not required).
Start with the sum of the two numbers being 24.
Note that if the two numbers were the same, they would be 12 and 12.
To get two numbers with the same sum of 24 but that differ by 4, take the 12 and 12, and add 2 to one of them and subtract 2 from the other. That will keep the sum the same; but the difference between the two numbers will be 2+2=4.
ANSWER: Their ages are 12+2=14 and 12-2=10.
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