Ana's age exceeds one-fifth of her dad's age by seven. In 19 years, her dad will be twice as old as her. How old is her dad now?
Pls, help! I think it is 17.5 or 19, but I'm not sure. :(
Pls Help!
A = d/5 + 7 ... 5A = d + 35 ... d = 5A - 35
2(A + 19) = d + 19 ... 2A + 38 = d + 19 ... d = 2A + 19
substituting ... 5A - 35 = 2A + 19
solve for A , then substitute back to find d
Now:
dad's age --- x
Ana's age --- y
y - x/5 = 7
y = x/5 + 7
Ana's age ---- (1/5)x + 7
19 years from now:
dad = x+19
Ana's age = (1/5)x + 7 + 19 = x/5 + 26
x+19 = 2(x/5 + 26)
x+19 = 2x/5 + 52
times 5, (don't like fractions)
5x + 95 = 2x + 260
3x = 165
x = 55
Her dad is now 55
check:
now her dad is 55
Ana is now 55/5 + 7 or 18 years
in 19 years:
dad is 74+19 = 74
ana = 18 + 19 = 37 , YES, here dad will be twice as old
a = Ana"s present age
d = dad's present age
Ana's age exceeds one-fifth of her dad's age by seven means:
a = d / 5 + 7
After 19 years Ana’s age will be a + 19 and Dad’s age will be d + 19
In 19 years, her dad will be twice as old as her means:
d + 19 = 2 ( a + 19 )
Since a = d / 5 + 7 replace
a with d / 5 + 7 in this equation
d + 19 = 2 ( d / 5 + 7 + 19 )
d + 19 = 2 ( d / 5 + 26 )
d + 19 = 2 d / 5 + 52
Subtract 19 to noth sides
d = 2 d / 5 + 33
Subtract 2 d / 5 to both sides
d - 2 d / 5 = 33
5 d / 5 - 2 d / 5 = 33
3 d / 5 = 33
Divide both sides by 3
d / 5 = 11
d = 55
a = d / 5 + 7 =
55 / 5 + 7 = 11 + 7 = 18
Ana is 18 yrs , Dad is 55 yrs old
To solve this problem, we can break it down into steps:
Step 1: Set up equations using the given information.
Let's assume Ana's current age is A, and her dad's current age is D.
According to the first sentence, "Ana's age exceeds one-fifth of her dad's age by seven." This can be represented as:
A = (1/5)D + 7
And according to the second sentence, "In 19 years, her dad will be twice as old as her." This can be represented as:
D + 19 = 2(A + 19)
Step 2: Solve the system of equations.
Now we need to solve the system of equations simultaneously to find the values of A (Ana's current age) and D (her dad's current age).
Substitute the value of A from the first equation into the second equation:
D + 19 = 2(((1/5)D + 7) + 19)
Simplify the equation:
D + 19 = 2((1/5)D + 26)
Distribute the multiplication:
D + 19 = (2/5)D + 52
Multiply through by 5 to eliminate the fraction:
5D + 95 = 2D + 260
Combine like terms:
5D - 2D = 260 - 95
Solve for D:
3D = 165
D = 55
Step 3: Find Ana's dad's age.
Now that we know the dad's age is 55, substitute this value into the first equation to find Ana's age:
A = (1/5)D + 7
A = (1/5) * 55 + 7
A = 11 + 7
A = 18
So, Ana's dad is currently 55 years old.