Jennie and Bill have a combined age of 50. 16 years ago Jennie was twice as old as Bill. Jennie is x and Bill is y.
i do not understand after this
x + y = 50
(x - 16) = 2(y - 16)
but i know the answer is x = 28 and y = 22
Please help
Jennie and Bill have a combined age of 50. 16 years ago Jennie was twice as old as Bill. Jennie is x and Bill is y.
i do not understand after this
x + y = 50
(x - 16) = 2(y - 16)
but i know the answer is x = 28 and y = 22
Please help
1--x + y = 50
2--(x - 16) = 2(y - 16) or
3--x - 2y = -16
4--Subtracting (3) from (1) yields
...3y = 66 making y = 22 and x = 28.
thankyou
To solve this problem, you need to set up a system of equations using the information provided.
Let's start by assigning variables to Jennie and Bill's ages. As given, let's say Jennie's age is represented by x, and Bill's age is represented by y.
We know that Jennie and Bill have a combined age of 50, so we can set up the equation: x + y = 50.
We also know that 16 years ago, Jennie was twice as old as Bill. This means that (x - 16) is equal to twice of (y - 16). Therefore, we can set up the equation: (x - 16) = 2(y - 16).
Now we have our system of equations:
Equation 1: x + y = 50
Equation 2: x - 16 = 2(y - 16)
To solve this system, we can use either substitution or elimination method. Let's use the substitution method:
From Equation 1, we can solve for x:
x = 50 - y
Now substitute this value of x into Equation 2:
50 - y - 16 = 2(y - 16)
Simplify the equation:
34 - y = 2y - 32
Combine like terms:
- y - 2y = - 32 - 34
- 3y = - 66
Divide both sides by -3:
y = (-66) / (-3)
y = 22
Now substitute the value of y back into Equation 1 to find the value of x:
x + 22 = 50
x = 50 - 22
x = 28
Therefore, the solution to the system of equations is x = 28 and y = 22. This means that Jennie is 28 years old, and Bill is 22 years old.