The number of bagels and coffee sold by a bagel shop yesterday can be modeled using the equation b+c=84. Their sales for the same day can be modeled using the equation 2b+c=145. Solve this system of equations using substitution. How many bagels and coffee were sold

There were 61 bagels and 23 coffee sold

Step-by-step explanation:

Let us solve the question

∵ The number of bagels and coffee sold by a bagel shop yesterday

   can be modeled using the equation b + c = 84

∴ b + c = 84 ⇒ (1)

∵ Their sales for the same day can be modeled using the equation

   2b + c = 145

∴ 2b + c = 145 ⇒ (2)

Let us solve the system of equations using substitution

→ Subtract the two sides of equation (1) by b to find c in terms of b

∵ b - b + c = 84 - b

∴ c = 84 - b ⇒ (3)

→ Substitute c in equation (2) by equation (3)

∵ 2b + 84 - b = 145

→ Add the like terms on the left side

∴ (2b - b) + 84 = 145

∴ b + 84 = 145

→ Subtract 84 from both sides

∵ b + 84 - 84 = 145 - 84

∴ b = 61

→ Substitute the value of b in equation (3) to find c

∵ c = 84 - 61

∴ c = 23

∴ There were 61 bagels and 23 coffee sold.

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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step-by-step explanation:

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