sum of ages of 3 son and father before 10 years is 220 then sum of their ages after 20 years will be
Answers
A man is 3 times as old as his son. The sum of their ages is 48 years. How old is the son?
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The son is 12 years old.
We can set up a system of equations as follows:
m=3s , since the man is 3 times as old as his son; hence, if we multiply the son’s age by 3, we will get the man’s age.
m+s=48 , since the sum of their ages is 48 years old.
Now, we just need to solve for s . There are three ways to solve a system of equations: by substitution, by elimination, and by graphing. The best and most efficient way to solve this one is by substitution.
We can replace the m in the second equation with 3s , because we already stated that m and 3s are equal in the first equation. We will obtain 3s+s=48 . This simplifies to 4s=48 . Divide both sides by 4, and we get s=12 .
If we solve by elimination, we can multiply one of the equations by −1 and add the equations together, therefore eliminating all the m terms. We can multiply either of the equations, since both have a coefficient of 1 for the m term.
If we multiply the first one,
m+s=48
−m=−3s
Add them, and we get
m+(−m)+s=48+(−3s)
m−m+s=48−3s
s=48−3s
4s=48
s=12
If we multiply the second one,
m=3s
−m−s=−48
Add them, and we get
m+(−m)−s=3s+(−48)
m−m−s=3s−48
−s=3s−48
−4s=−48
−s=−12
s=12
We can also solve by graphing. If we let m be the y axis and let s be the x axis, then our two equations are
y=3x
y+x=48 , which becomes y=−x+48
Graph both of them, and we get this:
The two graphs intersect at the point (12,36) , so the son’s age is 12 and the man’s age is 36.
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