A garden supply store sells two types of lawn mowers. The cashiers kept a tally chart for the total number of mowers sold. They tallied 30 mowers sold. Total sales of mowers for the year were $8379.70. The small mowers cost $249.99 and the large mowers cost $329.99. Find the number of each type of mower sold.
A.
The store did not sell any small mowers. They sold 25 large mowers.
B.
The store sold 8 small mowers and 22 large mowers.
C.
The store sold 11 small mowers and 19 large mowers.
D.
The store sold 8 more small mowers than large mowers
Small = 30 - Large
249.99S + 329.99L = 8379.70
Substitute 30-L for S in second equation and solve for L. Insert that value into the first equation and solve for S. Check by inserting both values into the second equation.
To solve this problem, we need to set up a system of equations using the given information.
Let's assume that the number of small mowers sold is represented by 'x' and the number of large mowers sold is represented by 'y'.
1. The total number of mowers sold is 30, so we have the equation:
x + y = 30
2. The total sales of mowers for the year is $8379.70, so we have the equation:
249.99x + 329.99y = 8379.7
Now, let's solve this system of equations to find the values of 'x' and 'y'.
We can solve this system of equations using the substitution or elimination method.
Let's use the elimination method:
Multiplying the first equation by 249.99, we have:
249.99x + 249.99y = 7499.7
Subtracting this equation from the second equation, we get:
329.99y - 249.99y = 8379.7 - 7499.7
Simplifying the equation, we have:
80y = 880
Dividing both sides of the equation by 80, we get:
y = 11
Substituting this value of y into the first equation, we have:
x + 11 = 30
Subtracting 11 from both sides of the equation, we get:
x = 19
Therefore, the number of small mowers sold is 19, and the number of large mowers sold is 11.
So, the correct answer is C. The store sold 11 small mowers and 19 large mowers.
To find the number of each type of mower sold, we can set up a system of equations. Let's define the following variables:
Let x be the number of small mowers sold.
Let y be the number of large mowers sold.
We know that the total number of mowers sold is 30, so we have the equation:
x + y = 30
We also know that the total sales from the mowers for the year were $8379.70. Since each small mower costs $249.99 and each large mower costs $329.99, we can set up another equation for the total sales:
249.99x + 329.99y = 8379.70
Now we can solve this system of equations to find the values of x and y.
We can start by multiplying the first equation by 249.99 so that the coefficients of x in both equations match:
249.99x + 249.99y = 7499.70
Now we have a system of equations:
249.99x + 249.99y = 7499.70
249.99x + 329.99y = 8379.70
Subtracting the first equation from the second equation, we eliminate the variable x:
329.99y - 249.99y = 8379.70 - 7499.70
80y = 880
y = 11
Substituting this value back into the first equation, we can find x:
x + 11 = 30
x = 19
Therefore, the store sold 19 small mowers and 11 large mowers.
The correct answer is option C. The store sold 11 small mowers and 19 large mowers.