An online furniture store sells chairs for $50 each and tables for $550 each. every day, the store can ship a maximum of 20 pieces of furniture and must sell at least $5000 worth of chairs and tables. if 9 chairs were sold, determine the minimum number of tables that the the store must sell in order to meet the requirements. if there are no possible solutions, submit an empty answer.
If 9 chairs were sold, the store must sell 11 tables in order to meet the requirements.
Selling price of each table = $50
Selling price of each table = $550
Let the number of chairs sold in a a day = x
Let Number of tables old in a a day = y
Hence, the selling price of x chairs = x times $50 = 50 x
and the selling price of y tables = y times $550 = 550 y
Maximum number of pieces that can be shipped = 20
⇒ x + y ≤ 20
Also, The total selling amount should at least be $5,000
⇒ 50 x + 550 y ≥ 5,000
Hence, the given system of equation is:
x + y ≤ 20
50 x + 550 y ≥ 5,000
Solving the given system:
put y = 20 - x from (1) in the equation (2), we get
50 x + 550 y = 5,000 ⇒ 50x + 550(20 -x) = 5000
or, 50x + 11,000 - 550x = 5000
or, -500x = -6000
x = 12
or the number of chairs sold at maximum = 12
also, y = 20- x = 20 - 12 = 8
So, number of tables sold at maximum = 8
Now, if the number of chairs sold = 9,
then the number of tables sold = 20 - 9 = 11
The selling amount is 50(9) + 550(11) = $6,500 > $5,000
Hence, 9 chairs were sold, the store must sell 11 tables in order to meet the requirements.
we'll this would mean that the dunk tank and the bounce house are the same for 20 hours because the 2 represents that the two activities, and the 20 represents the amount of hours they both are. so with this said, it means that the answer is c. the costs for a dunk tank and bounce house are the same for 20 hours.
c.the costs for a dunk tank and bounce house are the same for 20 hours.
hope this .
car 1 is exponential
car 2 is linear
note that dividing any value of car 1 over its previous year value leads to the same result. for example, (year2 value)/(year1 value) = 16346.60/17390 = 0.94; and also (year3 value)/(year2 value) = 15365.80/16346.60 = 0.9399997553008 which rounds to 0.94. the fact we get the same result each time suggests that we have an exponential model.
the value of car 2 drops by 1000 each time. this constant drop is why it's a linear function. put more technically, the slope is rise/run = -1000/1 = -1000. the negative rise means it's actually a fall in value.
equation for car 1 is f(x) = 18500(0.94)^x
equation for car 2 is f(x) = -1000x + 18500
in part a, we found that the multiplier was 0.94 by dividing any given value by its previous one. so this is the base of the exponential function, or the value of b. the value of 'a' is a = 18500 which is the starting amount. so we go from y = a*b^x to y = 18500*(0.94)^x. this is the equation for car 1.
now onto car 2's equation. in part a, we found car 2's value decrease at a constant rate of 1000 per yer. this was mentioned to be the slope, so m = -1000. the y intercept is the starting value so b = 18500. we go from y = mx+b to y = -1000x+18500
car 1's value after 9 years is $10,600.40
car 2's value after 9 years is $9,500.00
there isn't much of a significant difference in car value. however, i'm not sure what your teacher considers to be "significant". despite that, baxter is better off going with car 1 because it has higher value compared to car 2 after 9 years have passed.
plug x = 9 into each function. i'm going to make f(x) be the function for car 1 while g(x) be the function for car 2, to make comparison clearer.
f(x) = 18500(0.94)^x
f(9) = 18500(0.94)^9
f(9) = 18500(0.57299480222861)
f(9) = 10,600.4038412292
f(9) = 10,600.40
g(x) = -1000x+18500
g(9) = -1000(9)+18500
g(9) = -9000+18500
g(9) = 9,500.00