Six years ago the ratio of Rafaela and Leticia's ages was 3 is to 4, if in 4 years their ages in the relationship will be like 11 is to 13. What is Leticia's current age?
Let's assume Rafaela's age 6 years ago as R, and Leticia's age 6 years ago as L.
According to the given information, the ratio of their ages 6 years ago was 3:4.
So, we can write the equation: R/L = 3/4......(Equation 1)
After 4 years, Rafaela's age will be R+4, and Leticia's age will be L+4.
According to the second ratio, the relationship of their ages after 4 years is 11:13.
So, we can write the equation for that: (R+4)/(L+4) = 11/13.......(Equation 2)
To solve these two equations simultaneously, we can multiply equation 1 by (13L) and equation 2 by (4L).
Equation 1 becomes: 13R = 9L.......(Equation 3)
Equation 2 becomes: 44R + 52 = 52L + 48.......(Equation 4)
Now, we can substitute the value of R from equation 3 into equation 4:
44(9L/13) + 52 = 52L + 48
396L/13 + 52 = 52L + 48
396L + 676 = 676L + 624
280L = 52
L = 52/280
L = 0.1857
Therefore, Leticia's current age is 0.1857 * 100 = 18.57 years.
Approximately, Leticia's current age is 19 years.
Let's solve this problem step-by-step:
Step 1: Assign variables.
Let's assume Rafaela's age 6 years ago was R and Leticia's age 6 years ago was L.
Step 2: Use the given information to create equations.
According to the given information, the ratio of their ages 6 years ago was 3:4. So we have the equation: R/L = 3/4.
Step 3: Use the second given information to create another equation.
According to the second given information, in 4 years, their ages will be in the ratio of 11:13. So we have the equation: (R + 4)/(L + 4) = 11/13.
Step 4: Solve the equations simultaneously.
We can solve the equations simultaneously to find the values of R and L.
From the first equation, we can express R in terms of L: R = (3/4)L.
Now substitute this value of R in the second equation: (3/4)L + 4 / (L + 4) = 11/13.
Step 5: Solve for L.
Multiply both sides of the equation by (L + 4) to eliminate the denominator:
13(3L/4 + 4) = 11(L + 4).
Simplify the equation:
39L/4 + 52 = 11L + 44.
Multiply through by 4 to eliminate the fraction:
39L + 208 = 44L + 176.
Combine like terms:
39L - 44L = 176 - 208.
-5L = -32.
Divide both sides by -5:
L = -32/-5 = 32/5 = 6.4.
Step 6: Find Leticia's current age.
Leticia's current age is L + 6 (since 6 years have passed):
Leticia's current age = 6.4 + 6 = 12.4.
So, Leticia's current age is 12.4 years.