Sam and Harry are family. Sam is currently five times Harry's age. Sam's age is also 10 more than three times Harry's age. The following system of equations models this scenario:
x = 5y
x = 10 + 3y
What are their current ages?
We can use substitution to solve for their ages.
From the first equation, we know that x (Sam's age) is 5 times y (Harry's age).
Substitute x = 5y into the second equation:
5y = 10 + 3y
Subtract 3y from both sides:
2y = 10
Divide both sides by 2:
y = 5
Now that we know Harry is 5 years old, we can use the first equation to find Sam's age:
x = 5y = 5(5) = 25
Therefore, Sam is currently 25 years old and Harry is currently 5 years old.
To solve this system of equations for their current ages, we can use the method of substitution.
First, let's solve the first equation for x in terms of y:
x = 5y
Next, substitute this value of x into the second equation:
5y = 10 + 3y
Now, solve for y:
5y - 3y = 10
2y = 10
y = 5
Now, substitute this value of y back into the first equation to find x:
x = 5(5)
x = 25
Therefore, Harry is currently 5 years old, and Sam is currently 25 years old.
To solve this system of equations, you can use the method of substitution or elimination. Let's use substitution in this case.
We have the following equations:
x = 5y ---(1)
x = 10 + 3y ---(2)
We can substitute equation (1) into equation (2) to solve for the values of x and y.
Replacing x in equation (2) with 5y from equation (1), we get:
5y = 10 + 3y
Now we can solve for y:
5y - 3y = 10
2y = 10
Dividing both sides of the equation by 2, we find:
y = 5
Now that we know the value of y, we can substitute it back into equation (1) to find x:
x = 5 * 5
x = 25
Therefore, Harry is currently 5 years old and Sam is currently 25 years old.