Answer :
System of equations
STEP 1: setting the unkown variables
We want to find two values: the number of pieces sold at the original price and the number of pieces sold at the reduced price. Let's name those quantities:
x: number of pieces sold at the original price
y: number of pieces sold at the reduced price
STEP 2: writing the equations
First equation
We know that they sold 95 pieces. Then,
x + y = 95
Second equation
Each piece sold at the original price costs $14.50.
The earnings due to these pieces is given by the product of the number of them, x , and their cost:
14.50x
Each piece sold at the reduced price costs $12.50:
$14.50-$2.00 = $12.50
The earnings due to these pieces is given by the product of the number of them, y, and their cost:
12.50y
Then, the total earning is:
14.50x + 12.50y
We know that they took in $1237.50, then
14.50x + 12.50y = 1237.50
Then, the equations we are going to use are:
x + y = 95
14.50x + 12.50y = 1237.50
STEP 3: finding y
Using the equations we want to obtain an equation with just y unkown so we can find its value.
To do so we add each side of both equations, but first we convert the first so the result is an equation with just the y unkown:
Converting the first equation:
x + y = 95
↓ multiplying -14.50 both sides
-14.50(x + y) = -14.50 · 95
-14.50x - 14.50y = -1377.50
Then, the equations we are going to use are:
x + y = 95
14.50x + 12.50y = 1237.50
↓
-14.50x - 14.50y = -1377.50
14.50x + 12.50y = 1237.50
Now we add both sides of the two equations:
-14.50x - 14.50y = -1377.50
14.50x + 12.50y = 1237.50
__________________________
0x - 2.50y = -140
↓
- 2.50y = -140
Now we can find y, taking -2.50 to the right side of the equation
- 2.50y = -140
↓
- 2.50y/(-2.50) = -140/(-2.50)
y= -140/(-2.50)
y = 56
Then, the number of pieces sold at the reduced price is 56.
STEP 4: finding x
Since there were sold 95 pieces, then:
x = 95 - 56 = 39
x=39
Then, the number of pieces sold at the original price is 39.
