Portable Stereo
Portable Stereo
(BRAIN BUSTER) Your portable stereo requires 10 size....?
D batteries. You have $25 to spend on 5 packages of 2 batteries each and would like to maximize your battery power. Each regular package of batteries costs $4.25 and each alkaline package of batteries costs $5.50 (because alkaline batteries last longer). How many packages of each type of battery should you buy? Use a verbal model to write and solve a system of linear equations!
Let x = the number of packages of regular batteries
Let y = the number of packages of alkaline batteries
As for cost, 1 package costs 4.25, 2 packages cost 4.25*2, 3 cost 4.25*3, so in general the cost of purchasing x packages of batteries is 4.25x. The same can be said for y (5.50y)
You said you have $25 to spend on 5 packages, so this gives us two equations:
x+y = 5 (the total number of each type of battery package adds up to 5)
4.25x + 5.25y = 25 (the total cost of each type of battery package adds up to 25)
This is your system of equations. Solve the first one for y:
x+y = 5 (subtract x from both sides)
y = 5 - x
And plug that value for y into the second equation (this is called substitution)
4.25x + 5.50(5-x) = 25
Now distribute and simplify:
4.25x + 27.5 - 5.5x = 25 (distribute 5.5 across the parentheses)
-1.25x + 27.5 = 25 (combine 4.25x and -5.5x)
-1.25x = -2.5 (subtract 27.5 from both sides)
x = 2 (divide both sides by -1.25)
So according to this, you should buy 2 packages of regular batteries and 3 packages of alkaline batteries. Let's check the price:
4.25(2) + 5.50(3) = 8.50 + 16.50 = 25.
So it looks like that's the answer!
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