11.50-3.00=8.50
some of the pieces of pottery were sold at 11.50 and some of the pieces of pottery were sold at 8.50.
let x = number of pieces of pottery sold at 11.50.
let y = number of pieces of pottery sold at 8.50.
since a total of 99 pieces of pottery were sold, and since the total revenue collected was 931.50, you get the following equations.
x + y = 99
11.50 * x + 8.50 * y = 931.50
the first equation says that the total number of pieces of pottery sold was 99.
the second equation says that the total money collected was 931.50, when x were sold at 11.50 and y were sold at 8.50.
these two equations need to be solved simultaneously.
we'll solve by elimination.
multiply both sides of the first equation by 11.50 and leave the second equation as is to get:
11.5 * x + 11.5 * y = 1138.5
11.5 * x + 8.50 * y = 931.5
subtract the second equation from the first to get:
3.00 * y = 207
divide both sides of that equation by 3 to get y = 69.
since x + y = 99, this means that x has to be equal to 30.
your solution is that x = 30 and y = 69.
this means that the number of pieces of pottery sold at 11.50 is 30 and the number of pieces of pottery sold at 8.50 is 69.
30 * 11.50 + 69 * 8.50 is equal to 931.50.
solution looks good.
they sold 30 at the original price and 69 at the reduced price.
Answer:
x=0
Step-by-step explanation:
Answer:
see the attachments
Step-by-step explanation:
Actually, the given description fits 3 different triangles. They differ in the size of the included angle, hence the length of the remaining side. Possibilities are ...
- included angle: 91.5°; third side: 20.9
- included angle: 59.5°; third side: 14.6
- included angle: 20.5°; third side: 6.0
_____
When the non-included angle is opposite the long side, there is only one solution to the triangle. (See the first attachment.)
When the non-included angle is opposite the shorter of the given sides, there are generally two possible solutions. One of these has an acute angle opposite the long side; the other has an obtuse angle opposite the long side.
In any event, the Law of Sines is used to solve the triangle. First, the angle opposite the other given side is found; then the remaining angle and the side opposite it.
Suppose the given sides are "a" and "b", and the given angle is A. Then the Law of Sines tells you ...
B = arcsin(sin(A)·b/a) . . . . . possibly 2 values
From which ...
C = 180° -A -B
which allows finding ...
c = a·sin(C)/sin(A)
Vertical line is a way to determine whether a functin is a function or not.
5 8 5
25.96
x 1.9
————
23.364
25.960
1 1
23.364
+25.960
————
49.324