SOLUTION: Ricardo is 4 years less than twice as old as his sister. The sum of their ages is 20. How old is Ricardo?

Question 115449: Ricardo is 4 years less than twice as old as his sister. The sum of their ages is 20. How old is Ricardo?
Found 2 solutions by aka042, ganesh:
Answer by aka042(26) (Show Source): You can put this solution on YOUR website!
Let's call Ricardo's age 'r' and his sister's age 's'. The first part of the problem tells us that Ricardo is 4 years less than twice as old as his sister. "Twice as old" implies that we must multiply his sister's age by two, and then "4 years less" implies that we must subtract four years from that product.
Therefore, the first part of the problem leaves us with this equation:
Now, the problem tells us that the sum of their ages is 20. We can write this as .
Now, lets combine the two equations. The first equation tells us that because r = 2s -4, wherever we see r in the second equation, we can replace it with 2s -4. This gives us . To solve this equation, let's add four to both sides to give us , and now let's divide through by three to get .
This mean's his sister's age is 8. However, the problem is asking for Ricardo's age. So let's go back to our first equation that r = 2s - 4 and plug 8 in for s. . This implies that Ricardo's age is 12.
Let's just check to make sure. Ricardo is 4 years less than twice as old as his sister. 8 * 2 = 16, 16 - 4 =12, so that fits. Now let's just make sure the sum of their two ages is 20. 12 + 8 = 20, so that works to.
Therefore we conclude that Ricardo is 12 years old.
Answer by ganesh(20) (Show Source): You can put this solution on YOUR website!
Let age of Ricardo is x and age of his sister is y.
Ricardo is 4 years less than twice as old as his sister.
This can be written as x = 2y - 4.
That is, x - 2y = -4-----------(1)
The sum of their ages is 20.
This can be written as x + y = 20----------(2)
Solve (1) and (2).
(1) - (2) gives -3y = -24
That is, y = 8.
Therefore, x = 12.
Hence, Ricardo is 12 years old.

RELATED QUESTIONS
Ricardo is 4 years less than twice as old as his sister. The sum of their ages is 20.... (answered by stanbon)
Ricardo is 4 years less than twice as old as his sister. The sum of their ages is 20.... (answered by stanbon)
Ricardo is 4 years less than twice as old as his sister. The sum of their ages is 20.... (answered by joyofmath)
Ricardo is 4 years less than twice as old as his sister. The sum of their ages is 20.... (answered by checkley71)
Ricardo is 4 years less than twice as old as his sister. The sum of their ages is 20.... (answered by ptaylor)
Ricardo is 4 years less than twice as old as his sister. The sum of their ages is 20.... (answered by jim_thompson5910)
Ricardo is 4 years less than twice as old as his sister. The sum of their ages is 20.... (answered by ptaylor)
Ricardo is 4 years less than twice as old as his sister. The sum of their ages is 20.... (answered by stanbon)
RICARDO IS 4 YEARS LESS THAN TWICE AS OLD AS HIS SISTER. THE SUM OF THEIR AGES IS 20. (answered by elima)
Ricardo is 4 years less than twice as old as his sister. The sum of their ages is 20. How (answered by HyperBrain)