Translate each situation to a system of equations. Do not attempt to solve.
Paint Town sold 45 paintbrushes, one kind at $8.50 each and another at $9.50 each. In all, $398.75 was taken in for the brushes. How many of each kind were sold?
My teacher told me that I would probably have to make two equations and each one would have two variables.
I do not need to know how to solve, I just do not know how to make equations from the information provided.
Thanks!
Let x be the number of expensive paintbrushes and y be the number of inexpensive ones.
Clearly, x + y = 45 is one of the equations
The other equation says how much money was spent, expressed in terms of x and y.
___x + ___y = 38.75
Make an attempt at that. Fill in the blanks with the prices of each. Then solve the pair of equations
To create a system of equations for this problem, we can define variables to represent the unknown quantities. Let's say x represents the number of paintbrushes sold at $8.50 each, and y represents the number of paintbrushes sold at $9.50 each.
From the given information, we know that the total number of paintbrushes sold is 45. So, our first equation is:
x + y = 45
The second equation can be derived from the fact that the total amount of money collected from the sales was $398.75. The number of paintbrushes sold at $8.50 each (x) will contribute 8.50x to the total amount, and the number of paintbrushes sold at $9.50 each (y) will contribute 9.50y. Therefore, our second equation is:
8.50x + 9.50y = 398.75
These two equations form a system that represents the given information. Solving this system will give us the values of x and y, representing the number of each kind of paintbrush sold.