Half of Marimar's age added to one third of sergios age is 11 years.six years from now the sum of their ages will be 40 years. How old is each now?
i guess the answers are:
marimar: 10
sergio: 18
We don't "guess" in mathematics.
just translate the English to Math:
(1/2)m + (1/3)s = 11
times 6, the LCD
3m + 2s = 66 **
6 years from now:
(m+6) + (s+6) = 40
m + s = 28 ***
2 times *** ---> 2m + 2s = 56
subtract from **
m = 10
back in ***
10 + s = 28
s = 18
Marimar is now 10 and Sergio is now 18
check:
(1/2)(10) + (1/3)(18)
= 5+6 = 11 , check!
in 6 years:
16 + 24 = 40 , check!
oh sorry...hypothesis rather,,,an educated guess...:D
To solve this problem, we can set up a system of equations based on the given information.
Let's define Marimar's age as "M" and Sergio's age as "S".
From the first part of the problem, we know that "Half of Marimar's age added to one third of Sergio's age is 11 years," which can be expressed as:
(1/2)M + (1/3)S = 11 ----(Equation 1)
From the second part of the problem, we know that "six years from now the sum of their ages will be 40 years," which can be expressed as:
(M + 6) + (S + 6) = 40 ----(Equation 2)
Now, we have a system of two equations with two unknowns. We can solve it using various methods, such as substitution or elimination.
Let's solve this system using the substitution method:
Step 1: Solve Equation 1 for M in terms of S:
Multiply both sides of Equation 1 by 6 to get rid of the fractions:
3M + 2S = 66
Rearrange the equation to isolate M:
3M = 66 - 2S
M = (66 - 2S)/3 ----(Equation 3)
Step 2: Substitute Equation 3 into Equation 2:
Substitute (66 - 2S)/3 for M in Equation 2:
[(66 - 2S)/3 + 6] + (S + 6) = 40
Step 3: Simplify and solve for S:
Simplify the equation:
(66 - 2S + 18) + 3S + 18 = 120
66 + 18 + 18 - 120 = 2S - 3S
102 - 120 = -S
-18 = -S
S = 18
Step 4: Substitute the value of S back into Equation 3 to find M:
M = (66 - 2(18))/3
M = (66 - 36)/3
M = 30/3
M = 10
Therefore, Marimar is 10 years old and Sergio is 18 years old.