Answer:

first, transform the given to a mathematical statement.

let:

d= daughter's age

since the statement says that the mother's age is 4 years older(addition) than twice(multiplication) her daughter's age, therefore

2d+4= mother's age

the sum of their ages is 76.

2d+4+d=76

therefore, the algebraic equation would be

2d+4+d=76 or if simplified(meaning we combine like terms),

2d+4+d=76

3d+4=76

now, the algebraic equation is 3d+4=76.

if you are asked to solve for the equation,

3d+4=76

transpose 4 to the right side of the equation, meaning we'll change the sign to - 4 and add it to 76. considering the rule in adding negative-positive integers, the result will be 72.

3d=72

divide both sides by 3, in order to get the value of d.

d= 24.

the daughter's age is 24. now substitue the value of d to the mathematical expression for the mother's age.

2d+4

2(24)+4

48+4=52

the mother's age is 52, and her daughter is 24 years old.

we can check if the answer is correct by adding their age and check if we'll get 76.

52+24= 76.

the answer is correct.