A boy is 26 years younger than his father.In 3 years time, his age will be 1/3 his father's age.find the boys present age.
19 = (1/3) 45 ?
try again
f = b + 26 yes
b+3 = (1/3)(f+3) this was wrong
3 b + 9 = f+3
3 b - f = -6
3b -b - 26 = -6
2 b = 20
b = 10
f = 36
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now
13 = (1/3)(39)
yes
f=26+b...(1)
(b-3)=1/3(f-3)
3b-9=f-3
3b=f-3+9
3b=f+6
3b-6=f
3b-6=26+b
2b=26+6
2b=32
b=16
F=26+16
f=42
Let's assume that the boy's present age is x years.
According to the given information, the father's present age can be expressed as x + 26 years.
In 3 years' time, the boy's age will be x + 3 years, and his father's age will be (x + 26) + 3 years.
According to the second given piece of information, the boy's age in 3 years will be equal to one-third of his father's age in 3 years:
x + 3 = (1/3)(x + 26 + 3)
Using the distributive property:
x + 3 = (1/3)(x + 29)
Multiplying both sides of the equation by 3 to remove the denominator:
3(x + 3) = x + 29
Expanding the equation:
3x + 9 = x + 29
Subtracting x from both sides of the equation:
3x - x + 9 = 29
Simplifying:
2x + 9 = 29
Subtracting 9 from both sides of the equation:
2x = 29 - 9
Simplifying:
2x = 20
Dividing both sides of the equation by 2:
x = 10
Therefore, the boy's present age is 10 years.
To find the boy's present age, we can set up an equation based on the given information.
Let's assume the boy's present age is B, and his father's present age is F.
From the problem statement, we know that the boy is 26 years younger than his father. Therefore, we can write the equation:
B = F - 26 --- (1)
We are also given that in 3 years' time, the boy's age will be one-third of his father's age. In 3 years, the boy's age will be (B + 3), and the father's age will be (F + 3). So, we can write another equation:
B + 3 = (1/3) * (F + 3) --- (2)
To find the boy's present age, we need to solve these equations simultaneously. Here's how to do it:
Step 1: Substitute the value of B from equation (1) into equation (2).
(F - 26) + 3 = (1/3) * (F + 3)
Simplifying, we get:
F - 23 = (1/3) * (F + 3)
Step 2: Multiply both sides of the equation by 3 to remove the fraction:
3 * (F - 23) = F + 3
Simplifying, we get:
3F - 69 = F + 3
Step 3: Bring all the F terms to one side of the equation:
3F - F = 3 + 69
Simplifying, we get:
2F = 72
Step 4: Divide both sides of the equation by 2 to solve for F:
F = 36
Step 5: Substitute the value of F back into equation (1) to find B:
B = F - 26 = 36 - 26 = 10
Therefore, the boy's present age is 10 years.