Question 116313: Good evening ma'am or sir. Would you please help me in solving this word problem:
1). Renato is three years younger than Doming. Six years ago, Renato's age was two-thirds of Doming's age. What are their present ages?
Thank you ma'am or sir for your generosity in solving this problem.
Found 2 solutions by stanbon, bucky:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Renato is three years younger than Doming.
Let Doming's age be "x" yrs. old
Then Renato's age is "x-3" yrs old
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Six years ago, Renato's age was two-thirds of Doming's age.
Coming's age was "x-6" yrs old
Renato's age was "x-3-6"= "x-9" yrs old.
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What are their present ages?
EQUATION:
Renato was (2/3)Doming
x-9 = (2/3)(x-6)
x-9 = (2/3)x - 4
(1/3)x = 13
x = 39 (Doming's age NOW)
x-3 = 36 (Renato's age NOW)
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Cheers,
Stan H.
Answer by bucky(2189) (Show Source):
You can put this solution on YOUR website! Let R represent Renato's present age. Let D represent Doming's present age.
.
Since Renato is 3 years younger that Doming, this means that if we add 3 years to Renato's
age, the answer will equal Doming's age. In equation form this is:
.
R + 3 = D
.
6 years ago, how old was Renato? The answer to that is R - 6. And 6 years ago, how old was
Doming? The answer to that is D - 6. The problem tells you that at that time Renato's age
was two-thirds of Doming's age. So we can say:
.
R - 6 = (2/3)*(D - 6)
.
But we had an earlier equation that said R + 3 equals D. So in this equation we can substitute
R + 3 for D and get:
.
R - 6 = (2/3)*(R + 3 - 6)
.
Inside the second set of parentheses we can combine the +3 and the -6 to get -3. This makes
the equation become:
.
R - 6 = (2/3)*(R - 3)
.
Multiply out the right side and get:
.
R - 6 = (2/3)R - 2
.
You can get rid of the fraction by multiplying the entire equation (both sides and all terms) by
3 to get:
.
3R - 18 = 2R - 6
.
Get rid of the -18 on the left side by adding 18 to both sides and you have:
.
3R = 2R + 12
.
Get rid of the 2R on the right side by subtracting 2R from both sides and you have:
.
R = 12
.
So we can tell that Renato's present age is 12. And since Renato is 3 years younger than
Doming, that means that Doming is 15 years old.
.
Six years ago Renato was 12 - 6 or 6 years old. And six years ago Doming was 15 - 6 = 9 years old.
Renato's age at that time (6) was two-thirds of Doming's age (9), so that checks also.
The answers check ... Renato is presently 12 and Doming is presently 15.
.
Hope this helps you to understand the problem.
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