An older person is 5 years older than four times the age of a younger person. The sum of their ages is 30. Find their ages
Answers
Let's call X the age of the older person and Y the age of the younger person. We have 2 unknowns, therefore, we need 2 equations to solve for them:
1. The first equation is that the age of the older person, X, is 4 more than 5 times the age of the younger person, or:
X=4+5Y
2. The second equation is that the sum of the older persons age, X, and the younger persons age, Y, is 22, or:
X+Y=22
3. Substituting the first equation for X into the second equation we get:
(4+5Y)+Y=22 substituting 4+5Y for X
4+6Y=22 simplify
4+6Y-4=22-4 subtracting 4 from both sides
6Y=18 simplify
(6Y)/6=18/6 divide both sides by 6
Y=3 age of younger person
4. Now that Y is found, substitute 3 for Y in either equation to solve for X:
X+Y=22 original equation
X+3=22 substitute 3 for Y
X+3-3=22-3 subtract 3 from both sides
X=19 age of older person
5. After the answers are found check them in both equations:
X=4+5Y original equation X+Y=22 original equation
19=4+5(3) substituting 19 and 3 for X and Y 3+19=22 substituting for X and Y
19=4+15 simplify 22=22 check
19=19 check
Both equations check, therefore the math is correct and the answers are X=19 and Y=3.
Step-by-step explanation:
Ok
Answer
Age of younger person =5 years
Age of younger person =5 years Age of older person =25 years
Step by step explanation
Let the age of younger person be x.
Age of older person = 5+4x
Sum of there ages = 5+4x+x=30
= 5+5x=30
=5x= 30-5
=5x=25
=x=25/5
= x=5
Age of younger person = x = 5 years
5 years Age of older person = 5+4x=5+4(5)
=5+20
=25 years
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