An artist is going to sell two sizes of prints at an art fair. The artist will charge $20 for the small print and $45 for a large print. The artist would like to sell twice as many small prints as large prints. The booth the artist is renting for the day cost $510. How many of each size print must the artist sell in order to break even at the fair?
20x(2) + 45x = $510
40x + 45x =$510
85x / 85 = $510/85
x = 6
She sold twice as many small than large. So, small = 2(6) which equals 12
20(12) + 45(6) = $510
240 + 270 = $510
number of small prints --- x
number of large prints --- 2x
20x + 45(2x) = 510
20x+90x=510
110x = 510
x= 510/110 = 4.6
but you can't sell .6 of a print, so I would say he should sell 5 small and 10 large prints
check:
5(20) + 10(45) = 550 -- a profit
if he sold only 4 small and 8 large
income = 4(20) = 8(45) = 440 , not enough to cover rent.
You switched the large and small print numbers. Selling twice as many small prints would make it:
20 (2x) + 45 (x) = 510
If you solve with that formula in mind, x = 6...and that is the break-even number.
hi I THINK THE ANSWER IS 569
12 smalls 6 larges
12 small 6 large
To answer this question, we will need to set up an equation and solve it using algebra.
Let's assume the artist sells x small prints and y large prints.
According to the given information, the artist charges $20 for each small print and $45 for each large print. Thus, the revenue from selling small prints is 20x, and the revenue from selling large prints is 45y.
The artist wants to sell twice as many small prints (x) as large prints (y). So, we can write the equation as:
x = 2y
Now we need to calculate the total revenue, which should cover both the cost of renting the booth and the price of the prints. The cost of renting the booth is $510.
The total revenue can be calculated by multiplying the number of small prints by their price and the number of large prints by their price:
Total Revenue = (Price of Small Print × Number of Small Prints) + (Price of Large Print × Number of Large Prints)
Total Revenue = (20x) + (45y)
To break even, the total revenue should cover the booth cost:
Total Revenue = Booth Cost
(20x) + (45y) = 510
Now we have a system of equations:
x = 2y
(20x) + (45y) = 510
To solve this system, we can substitute the value of x from the first equation into the second equation:
20(2y) + 45y = 510
40y + 45y = 510
85y = 510
y = 510/85
y = 6
Now, substitute the value of y back into the first equation to find x:
x = 2(6) = 12
Therefore, the artist needs to sell 12 small prints and 6 large prints in order to break even at the art fair.