the sum of the ages of two siblings is 23 and the difference between their ages is 7. if frank is the older brother of beth, determine their ages by creating a pair of simultaneous equations and solving them.
this is killing me i have been working on it for hours. can only us substitution method or elimination.
letting x be the age of frank
y be the age of beth;
x+y=23......(equation 1)
x-y=7 .......(equation 2)
using substitution method,
x=7+y
(7+y)+y=23
7+2y=23
2y=23-7
2y=16
y=8 x=7+8
=15
frank (x)=15years
beth (y) =8years
Amazing website. very helpful and easy to found the correct answer.
Oh, the age mystery! Don't worry, I'm here to help you clown around with these equations! Let's solve this age puzzle step by step using the substitution method, shall we?
Let's call Frank's age 'F' and Beth's age 'B'. We have two pieces of information: first, the sum of their ages is 23 → F + B = 23. Second, the difference between their ages is 7, which means Frank is 7 years older than Beth → F - B = 7.
Now, let's solve it by substitution!
From the second equation, we can rewrite it as F = B + 7.
Now we can substitute F in the first equation with B + 7 → (B + 7) + B = 23.
Expanding the equation, we have:
2B + 7 = 23.
2B = 23 - 7.
2B = 16.
B = 8.
Now that we know Beth's age is 8, we can substitute this back into our equation F = B + 7 → F = 8 + 7 → F = 15.
Therefore, Frank is 15 years old and Beth is 8 years old.
Ta-da! The age mystery is solved!
Let's solve the problem step-by-step using the substitution method:
Step 1: Assign variables
Let's assume the age of Frank is "F" and the age of Beth is "B".
Step 2: Write equations
According to the given information:
1. The sum of their ages is 23:
F + B = 23
2. The difference between their ages is 7:
F - B = 7
Step 3: Solve by substitution
From the second equation, we can isolate F:
F = B + 7
Now substitute this value of F into the first equation:
(B + 7) + B = 23
Simplify the equation:
2B + 7 = 23
Move 7 to the other side:
2B = 16
Divide both sides by 2:
B = 8
Now substitute the value of B back into one of the original equations:
F + 8 = 23
Simplify the equation:
F = 23 - 8
F = 15
Step 4: Determine the ages
Frank is 15 years old (F = 15) and Beth is 8 years old (B = 8).
Therefore, Frank is the older brother and is 15 years old, while Beth is the younger sister and is 8 years old.
To solve this problem using simultaneous equations, let's denote the age of Frank as F and the age of Beth as B.
We are given two important pieces of information:
1. The sum of their ages is 23: F + B = 23
2. The difference between their ages is 7: F - B = 7
To solve this system of equations using the substitution method, we can isolate one variable in one equation and substitute it into the other equation. Let's solve for F in terms of B in the second equation.
From the second equation, we have: F - B = 7
Adding B to both sides, we get: F = B + 7
Now, we can substitute this expression for F into the first equation: (B + 7) + B = 23
Simplifying the equation, we get: 2B + 7 = 23
Subtracting 7 from both sides: 2B = 16
Dividing both sides by 2: B = 8
Now that we know Beth's age is 8, let's substitute this value back into one of the original equations to find Frank's age. Using the first equation: F + 8 = 23
Subtracting 8 from both sides: F = 15
Therefore, Beth is 8 years old and Frank is 15 years old.
You can also solve this system of equations using the elimination method. Let's rewrite the equations:
Equation 1: F + B = 23
Equation 2: F - B = 7
To eliminate one variable, we can add the two equations together. This eliminates the B terms:
(F + B) + (F - B) = 23 + 7
2F = 30
F = 15
Substituting F = 15 back into Equation 2:
15 - B = 7
B = 8
Again, we find that Beth is 8 years old and Frank is 15 years old.
Both methods will yield the same solution.