Question 812440: A color cartridge for xt-100 inkjet printer is $5 more than twice the price of a black ink cartridge. If you can buy both cartridge for a total of $43.50, what is the cost of the color cartridge?
Answer by jsmallt9(3758)   (Show Source):
You can put this solution on YOUR website! We have two unknowns: the price of a color cartridge and the price of a black ink cartridge. First we will use two variables for these unknowns so we will need two equations.
Let c = price of a color cartridge
Let b = the price of a black ink cartridge.
From "A color cartridge for xt-100 inkjet printer is $5 more than twice the price of a black ink cartridge." we get:
c = 5 + b
From "you can buy both cartridge for a total of $43.50" we get:
c + b = 43.50
There are many ways to solve such a system. Since the first equation is already solved for c, we can easily use the Substitution Method. Using the expression from the first equation we can substitute for c in the second equation:
(5 + b) + b = 43.50
Now we solve for the remaining variable, b. First we simplify the left side:
5 + 2b = 43.50
Subtract 5:
2b = 38.50
Divide by 2:
b = 19.25
So a black ink cartridge costs $19.25. But we are asked for the price of a color cartridge. So we use this result and either of the original equations to find c:
c = (19.25) + 5
which simplifies to:
c = 24.25
So a color cartridge costs $24.25.
P.S. This problem could also have been solved using a single variable. Since we know what the combined price of the cartridges is, $43.50, we can use:
Let c = the price of a color cartridge.
Then
43.50 - c = the price of a black ink cartridge.
With one variable we only need one equation. From "A color cartridge for xt-100 inkjet printer is $5 more than twice the price of a black ink cartridge." we get:
c = 5 + (43.50 - c)
Simplifying the right side:
c = 48.50 - c
Adding c:
2c = 48.50
Dividing by 2:
c = 24.25
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