the sum of ages of maria and anna is 35. when maria was two-thirds her present age and anna was three fourths of her present ages, the sum of their ages was 25. how old is maria now?
turn the words into math:
m+a = 35
2/3 m + 3/4 a = 25
now just crank it out
15
Let's assume Maria's present age is M, and Anna's present age is A.
According to the given information:
1) The sum of their ages is 35:
M + A = 35
2) When Maria was two-thirds her present age and Anna was three-fourths her present age, the sum of their ages was 25:
(M - (2/3)M) + (A - (3/4)A) = 25
Simplifying equation 2:
(1/3)M + (1/4)A = 25
Multiply equation 1 by 4 and equation 2 by 12 to eliminate fractions:
4M + 4A = 140
4M + 3A = 300
Subtracting equation 1 from equation 2:
(4M + 3A) - (4M + 4A) = 300 - 140
-A = 160
A = -160
Since a negative age doesn't make sense, there seems to be an error in the given information or the problem itself. Please double-check the problem statement and provide the correct information.
To solve this problem, let's first assign variables to the unknowns. Let's say Maria's present age is M, and Anna's present age is A.
We are given two pieces of information:
1) The sum of their ages is 35:
M + A = 35 (Equation 1)
2) When Maria was two-thirds her present age and Anna was three-fourths her present age, their sum of ages was 25:
(M - (2/3)M) + (A - (3/4)A) = 25
Simplifying this equation:
(1/3)M + (1/4)A = 25 (Equation 2)
Now we have a system of two equations with two unknowns. We can solve this system by substitution or elimination. Let's use substitution.
Solve Equation 1 for A:
A = 35 - M
Substitute this value of A in Equation 2:
(1/3)M + (1/4)(35 - M) = 25
Multiply through by 12 to eliminate the fractions:
4M + 3(35 - M) = 300
4M + 105 - 3M = 300
M + 105 = 300
M = 300 - 105
M = 195
So, Maria is 195 years old now.
Please note that this calculation assumes that both Maria and Anna have positive integer ages.