Question 1203623: jack is 7 years older than mia. the sum of there ages is 53.how old is jack.
Found 5 solutions by mananth, Alan3354, greenestamps, josgarithmetic, ikleyn:
Answer by mananth(16949)   (Show Source):
You can put this solution on YOUR website! jack is 7 years older than mia. the sum of there ages is 53.how old is jack.
Let mia's age be x years
Jack is 7 years older
so his age will be x+7 years
sum of there ages is 53
x+(x+7)=53
2x+7 =53
2x=53-7
2x = 46
x=23
mia is 23 years old
so Jack is 23+7 = 30 years old
Answer by Alan3354(69443)  (Show Source):
You can put this solution on YOUR website! jack is 7 years older than mia. the sum of there ages is 53.how old is jack.
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J - M = 7
J + M = 53
---------------------- Add
2J = 60
J = 30
M = 23
Answer by greenestamps(13295)  (Show Source):
You can put this solution on YOUR website!
You have received two good formal algebraic solutions, one using two variables and the other using one. I myself nearly always find using a single variable is easier... but it is a personal choice for each student.
If formal algebra is not required, a quick mental solution can be good problem-solving exercise.
The sum of their ages is 53, and one of them is 7 years older than the other.
So subtract 7 from the age of the older person; that subtracts 7 from the sum of their ages.
That leaves you with two people with the same age, and the sum of their ages is 63-7 = 56; so each of them is 56/2 = 28 years old.
Now add the 7 years back on to the older person's age to find the two ages are 28 and 28+7 = 35.
ANSWER: Jack (the older) is 35 years old
Answer by josgarithmetic(39736)  (Show Source):
Answer by ikleyn(53618)  (Show Source):
You can put this solution on YOUR website! .
Jack is 7 years older than Mia. The sum of  their ages is 53. How old is Jack.
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Again, it is nice problem to solve it MENTALLY in 6 seconds, without using equations.
Indeed, consider/imagine another person Jack' instead of Jack, who (Jack') is 7 years younger than Jack.
Then Jack' and Mia both are of the same age, and the sum of their ages is 53-7 = 46.
Hence, Jack' is 46/2 = 23 years old.
It implies that Jack, the true person, is 23 + 7 = 30 years old.
At this point, the solution is complete.
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