the sum of the age of a girl and her brother is 26 year 3 years ago her age was 4 time the age of her brother. find their present age?
g = girls age
b = boys age
g + b = 26 Subtract b to both sides
g + b - b = 26 - b
g = 26 - b
g - 3 = 4 ( b - 3 )
26 - b - 3 = 4 ( b - 3 )
23 - b = 4 b - 12 Add b to both sides
23 - b + b = 4 b + b - 12
23 = 5 b - 12 Add 12 to both sides
23 + 12 = 5 b - 12 + 12
35 = 5 b Divide both sides by 5
35 / 5 = 5 b / 5
7 = b
b = 7
g = 26 - b
g = 26 - 7
g = 19
Ah, the age-old question of sibling arithmetic. Let me put on my counting clown shoes and calculate this for you.
Let's give the girl's age a variable, shall we? Let's call it "G" for girl. And her brother's age will be "B" for brother. Since we know the sum of their ages is 26, we can write it as an equation:
G + B = 26
Now, we also know that 3 years ago, the girl's age was 4 times her brother's age. Let's write that down too:
G - 3 = 4(B - 3)
Now, we have two equations! Two equations for the price of one! But since we're in a humorous mood, let's take the second equation and simplify it a bit:
G - 3 = 4B - 12
G = 4B - 12 + 3
G = 4B - 9
Now that we have a simplified version, let's substitute it back into the first equation:
(4B - 9) + B = 26
5B - 9 = 26
5B = 26 + 9
5B = 35
B = 35 / 5
B = 7
Huzzah! We've found the brother's age: 7 years old. Now, let's substitute it back into the first equation to find the girl's age:
G + 7 = 26
G = 19
So, the girl is 19 years old. The present ages are 19 for the girl and 7 for the brother!
Remember, clown math is always the most fun math.
Let's solve this problem step by step.
Step 1: Assign variables to the unknowns.
Let's say the girl's age is "G" and her brother's age is "B".
Step 2: Translate the given information into equations.
The sum of their ages is 26: G + B = 26.
Three years ago, the girl's age was 4 times her brother's age: G - 3 = 4(B - 3).
Step 3: Solve the equations simultaneously.
From equation 1, we can write G = 26 - B.
Substituting this value of G into equation 2, we get (26 - B) - 3 = 4(B - 3).
Simplifying further, we have 23 - B = 4B - 12.
Bringing the terms containing B together, we get 4B + B = 23 + 12.
Combining like terms, we have 5B = 35.
Dividing both sides by 5, we find that B = 7.
Substituting the value of B into equation 1, we find G = 26 - 7 = 19.
Step 4: Check the solution.
We have G = 19 and B = 7.
Three years ago, the girl was 16 (19 - 3), and her brother was 4 (7 - 3).
Indeed, the girl's age three years ago was 4 times her brother's age.
Therefore, the present ages of the girl and her brother are 19 and 7, respectively.
To find the present age of the girl and her brother, we can set up a system of equations using the given information.
Let's denote the girl's age as G and the brother's age as B.
From the first statement, we know that the sum of their ages is 26:
G + B = 26 ----- Equation 1
From the second statement, we know that three years ago, the girl's age was four times the age of her brother:
(G - 3) = 4(B - 3)
Simplifying this equation, we get:
G - 3 = 4B - 12
G = 4B - 9 ----- Equation 2
Now we have a system of equations with two variables (G and B). We can use these equations to solve for their present ages.
To solve the system of equations, we can use the substitution method or the elimination method. Let's use the substitution method in this case.
Step 1: Solve Equation 2 for G in terms of B:
G = 4B - 9
Step 2: Substitute G in Equation 1 with the expression 4B - 9:
4B - 9 + B = 26
Step 3: Simplify the equation:
5B - 9 = 26
Step 4: Add 9 to both sides of the equation:
5B = 35
Step 5: Divide both sides by 5:
B = 7
Now that we have the value of B, we can substitute it back into Equation 1 to determine G:
G + 7 = 26
G = 19
Therefore, the girl's present age is 19 and the brother's present age is 7.