you purchase 8 video game machines for a total of $2722. A nintendo costs $249 and an Xbox costs $395. How many nintendos and how many xboxes did you buy?
What 2 equations do I write and how do i solve it? (elimination substituation etc.)
x+y = 8
249 x + 395 y = 2722
try substitution
y = (8-x)
then
249 x +395(8-x) = 2722
To solve this problem, you can set up a system of equations using the given information. Let's assume you bought 'x' Nintendos and 'y' Xboxes.
Equation 1: The number of Nintendos (x) and Xboxes (y) purchased is equal to 8 video game machines.
x + y = 8
Equation 2: The total cost of the Nintendos (x) and Xboxes (y) purchased is $2722.
249x + 395y = 2722
To solve this system of equations, you have a few options:
1. Substitution method: Solve one equation for one variable and substitute it into the other equation.
2. Elimination method: Multiply one or both equations by appropriate factors to make the coefficients of one variable the same, allowing you to eliminate that variable when adding/subtracting equations.
3. Matrix method: Represent the system as a matrix equation and solve using matrix operations.
Let's solve the system using the elimination method:
Multiply Equation 1 by 249 to make the coefficients of 'x' in both equations equal:
(249)(x + y) = 8(249)
249x + 249y = 1992
Now, subtract this new equation from Equation 2 to eliminate 'x':
(249x + 395y) - (249x + 249y) = 2722 - 1992
(395y - 249y) = 730
146y = 730
y = 5
Substitute the value of 'y' back into Equation 1 to find 'x':
x + 5 = 8
x = 8 - 5
x = 3
Therefore, you bought 3 Nintendos and 5 Xboxes.