Jose has 200 baseball cards. He has the Topps brand which he paid $1.50 each, Upper Deck Company brand which he paid $5.75 each, and Panini Group brand which he paid $2.60 each. He has 20 fewer Upper Deck Company brand than Panini Group brand. The total amount he spent was $589.50. How many of each brand of baseball cards does he have?

Jose has 70 Panini, 50 Upper Deck, and 80 Topps cards.

Step-by-step explanation:

Given that Jose has 200 baseball cards, and he has the Topps brand which I have paid $ 1.50 each, Upper Deck Company brand which I have paid $ 5.75 each, and Panini Group brand which I have paid $ 2.60 each, and he has 20 fewer Upper Deck Company brand than Panini Group brand, and the total amount he spent was $ 589.50, to determine how many of each brand of baseball cards does he have, the following calculation must be performed:

100 Panini + 80 Upper Deck + 20 Topps = X

100 x 2.6 + 80 x 5.75 + 20 x 20 x 1.5 = X

260 + 460 + 30 = X

X = 750

80 Panini + 60 Upper Deck + 60 Topps = X

80 x 2.6 + 60 x 5.75 + 60 x 1.5 = X

208 + 345 + 90 = X

X = 643

60 Panini + 40 Upper Deck + 100 Topps = X

60 x 2.6 + 40 x 5.75 + 100 x 1.5 = X

156 + 230 + 150 = X

X = 536

70 Panini + 50 Upper Deck + 80 Topps = X

70 x 2.6 + 50 x 5.75 + 80 x 1.5 = X

182 + 287.5 + 120 = X

X = 589.5

Therefore, Jose has 70 Panini, 50 Upper Deck, and 80 Topps cards.

x = central angle apc = measure of minor arc ac

the two angles x and 30 add to 180, so x+30 = 180 and x = 180-30 = 150. the measure of minor arc ac is 150 degrees.

what we need to do from here is find the circumference and then multiply it by x/360 since there are 360 degrees in a circle. in this case, x = 150, so x/360 = 150/360 = 15/36 = 5/12. the shortest distance along the curve from a to c is 5/12 of the distance around the entire circle (aka circumference)

c = circumference

c = pi*d

c = pi*24

c = 24pi

now multiply this by 5/12 to get

distance along minor arc ac = (5/12)*(circumference)

distance along minor arc ac = (5/12)*(24pi)

distance along minor arc ac = 10pi

the formula you can use is

l = (x/360)*pi*d

with

l = length of minor arc

x = central angle

d = diameter

which essentially is the steps we took though a bit differently.

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