Bert is 5 years older than twice the age of mario. Nine years ago, the sum of their ages is 50. How old is each now?
present:
Mario's age --- x
Bert's age ----- 2x+5
Nine years ago:
Mario --- x-9
Bert ---- (2x+5) - 9 = 2x -4
"Nine years ago, the sum of their ages is 50. "
----> x-9 + 2x-4 = 50
3x = 63
x = 21
Mario is now 21 and Bert is now 47
check:
9 yrs ago Mario was 12 and Bert was38
Is 12+38 = 50?
YES, all is good!
Brendan is 4 years older than Ariana. In 3 years the sum of their ages will be 56. How old is Brendan now?
To solve this problem, you can use a system of equations. Let's denote the age of Mario as "m" and the age of Bert as "b".
According to the problem, Bert is 5 years older than twice the age of Mario. So, we can write the equation:
b = 2m + 5
Nine years ago, the sum of their ages was 50. This means that their combined age nine years ago was 50. So, we have another equation:
(m - 9) + (b - 9) = 50
Now, we can substitute the value of b from the first equation into the second equation:
(m - 9) + ((2m + 5) - 9) = 50
Simplifying this equation, we get:
m - 9 + 2m - 4 = 50
3m - 13 = 50
To isolate the variable "m", we'll add 13 to both sides of the equation:
3m = 50 + 13
3m = 63
And then divide both sides of the equation by 3:
m = 63 / 3
m = 21
Now that we know the age of Mario is 21, we can substitute this value back into the first equation to find Bert's age:
b = 2m + 5
b = 2(21) + 5
b = 42 + 5
b = 47
Therefore, Mario is currently 21 years old, and Bert is currently 47 years old.