Answer
The answer is: the most expensive battery costs 195 dollars, the least expensive battery costs 65 dollars and the third battery costs 80 dollars.
Work Step by Step
We assign the variables:
x = most expensive battery
y = least expensive battery
z= the third battery
Step 1:
Find the equations that represent the problem.
We know that $x+y+z=340$ because the addition of the prices of each battery has to equal the total cost of the three batteries.
$x+y+z=340$ -> Eq. 1
We can get the second equation from the wording in the problem.
From "The most expensive battery is three times the cost of the least expensive", we get
$x=3y$ -> Eq. 2
We can get the third equation from the wording in the problem.
From "The third is 15 dollars more than the least expensive.",
$z=y+15$ -> Eq. 3
Step 2:
Solve the system of equations. Using the substitution method,
-> Substitute Eq. 2 and Eq. 3 into Eq. 1
$3y+y+y+15=340$
$5y=340-15$
$5y=325$
$y=\frac{325}{5}$
$y=65$
-> Substitute the value for $y$ into Eq. 2 and Eq. 3
Into Eq. 2
$x=3(65)$
$x=195$
Into Eq. 3
$z=65+15$
$z=80$
Step 3:
The answer is: the most expensive battery costs 195 dollars, the least expensive battery costs 65 dollars and the third battery costs 80 dollars.
