Deborah is x years old and Sarah is y years old. The sum of their age is 58. If Deborah is 4 years younger than Sarah. Find the age of both women
Simultaneous equation:
x + y = 58
x = y - 4
Substitute x in the first equation:
y - 4 + y = 58
2y = 62
y = 31
Substitute y in the second equation:
x = 31 - 4
x = 27
Therefore, Deborah is 27 years old and Sarah is 31 years old.
To find the age of both Deborah and Sarah, let's break down the problem step by step:
1. We are given that Deborah is x years old and Sarah is y years old.
2. The sum of their ages is 58, so we can write the equation: x + y = 58.
3. We also know that Deborah is 4 years younger than Sarah, which can be expressed as: x = y - 4.
4. Now, we can substitute the value of x from the second equation into the first equation: (y - 4) + y = 58.
5. Simplifying the equation, we have: 2y - 4 = 58.
6. Adding 4 to both sides of the equation, we get: 2y = 62.
7. Dividing both sides of the equation by 2, we find: y = 31.
8. Finally, we substitute the value of y back into the equation x = y - 4: x = 31 - 4, x = 27.
Therefore, Deborah is 27 years old and Sarah is 31 years old.
Let's solve the problem step-by-step:
Step 1: Setting up the equations.
Let's assign variables to the unknown ages:
Deborah's age: x
Sarah's age: y
We are given the following information:
1. The sum of their ages is 58: x + y = 58
2. Deborah is 4 years younger than Sarah: x = y - 4
Step 2: Substitution.
Substitute the value of x from equation 2 into equation 1:
(y - 4) + y = 58
Step 3: Simplify.
Combine like terms and solve for y:
2y - 4 = 58
2y = 58 + 4
2y = 62
y = 62/2
y = 31
Step 4: Solve for x.
Substitute the value of y into equation 2:
x = y - 4
x = 31 - 4
x = 27
Step 5: Answer.
Deborah is 27 years old and Sarah is 31 years old.