Final answer:
Lisa is 18 years old and Jessica is 25 years old.
Step-by-step explanation:
To solve this problem, let's assign variables to represent Lisa's and Jessica's ages. Let L be Lisa's age and J be Jessica's age.
We are given two equations: Twice Lisa’s age is 11 more than Jessica’s age and the sum of Lisa’s age and Jessica's age is 43.
The first equation can be written as 2L = J + 11, and the second equation is L + J = 43. We can solve this system of equations to find the ages of the girls.
First, let's solve the second equation for L: L = 43 - J.
Substitute this expression for L in the first equation: 2(43 - J) = J + 11.
Simplify the equation: 86 - 2J = J + 11.
Combine like terms: 86 - 11 = J + 2J. This simplifies to 75 = 3J.
Divide both sides by 3: J = 25.
Substitute this value for J in the second equation: L + 25 = 43.
Subtract 25 from both sides: L = 18.
Therefore, Lisa is 18 years old and Jessica is 25 years old.
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