beth is two years older than julio.Gerald is twice as old as beth.debra is twice as old as gerald.the sum of theIr ages is 38.how old is beth?
B=age of Beth,
J=age of Julio
G=age of Gerald
D=age of Debra
Equations, expressed in terms of J
B=J+2
G=2B=2(J+2)=2J+4
D=2G=2(2J+4)=4J+8
Finally
J+B+G+D=38 and substitute above values:
J+(J+2)+(2J+4)+4J+8=38
8J+14=38
J=3
Backsubstitute J in the above equations to get the ages of Beth, Gerald and Debra.
To find out how old Beth is, we can break down the information given and use algebra to solve for Beth's age.
Let's assign variables to each person's age:
Julio's age: x
Beth's age: x + 2 (as Beth is two years older than Julio)
Gerald's age: 2 * (x + 2) = 2x + 4 (as Gerald is twice as old as Beth)
Debra's age: 2 * (2x + 4) = 4x + 8 (as Debra is twice as old as Gerald)
From the given information, we know that the sum of their ages is 38:
x + x + 2 + 2x + 4 + 4x + 8 = 38
Combining like terms:
8x + 14 = 38
Subtracting 14 from both sides:
8x = 24
Dividing both sides by 8:
x = 3
Now that we know Julio's age is 3, we can find Beth's age:
Beth's age = Julio's age + 2 = 3 + 2 = 5
Therefore, Beth is 5 years old.