A garden supply store sells two types of lawn mowers. The smaller mower costs $249.99 and the larger mower cost $329.99. If 30 total mowers were sold and the total sales for a given year was $8379.70, find how many of each type were sold. Find the coordinate pair solution with no spaces in the answer.
Let's say the number of smaller mowers sold is x and the number of larger mowers sold is y.
We can set up a system of equations to represent the given information:
x + y = 30 (equation 1, representing the total number of mowers sold)
249.99x + 329.99y = 8379.70 (equation 2, representing the total sales amount)
To solve this system of equations, we can use the method of substitution.
From equation 1, we have y = 30 - x.
Substituting this into equation 2, we get:
249.99x + 329.99(30 - x) = 8379.70
249.99x + 9899.70 - 329.99x = 8379.70
-80x = -1520
x = 19
Substituting this value of x back into equation 1, we get:
19 + y = 30
y = 11
Therefore, 19 small mowers and 11 large mowers were sold.
The coordinate pair solution is (19,11).