Tasty bakery sells three kinds of muffins chocolate chip muffins at 15 cents each, oatmeal muffins at 20 cents each, and cranberry muffins at 25 cents each. charles buys some of each kind and chooses three times as many cranberry muffins as chocolate chip muffins. if he spends $3.70 on 17 muffins, how many cranberry muffins did he buy?

9

Step-by-step explanation:

Let c = number of chocolate chip muffins.

Let a = number of oatmeal muffins

Let r = number of cranberry  muffins

He bought 17 muffins, so

c + a + r = 17

Using the prices, the following equation shows how much he spent,

0.15c + 0.2a + 0.25r = 3.70

Charles buys some of each kind and chooses three times as many cranberry muffins as chocolate chip muffins.

r = 3c

We substitute 3c for r in the first two equations.

c + a + r = 17

c + a + 3c = 17

a + 4c = 17           Eq. 1

0.15c + 0.2a + 0.25r = 3.70

0.15c + 0.2a + 0.25(3c) = 3.70

0.15c + 0.2a + 0.75c = 3.70

0.2a + 0.9c = 3.70

2a + 9c = 37      Eq. 2

Equations 1 and 2 are two equations in two unknowns.

a + 4c = 17

2a + 9c = 37

Multiply the first equation just above by -2 and add it to the second equation.

   -2a - 8c = -34

+    2a + 9c = 37

               c = 3

r = 3c = 3(3) = 9

9 cranberry muffins

(sin 42)/31. = sinx)/37

sinx = 37 (sin42)/31

= 37× 0.66/31 = 0.787

x= 51.9

other angle opposite to y = 180-51.9-42

= 180- 93.9 =86.1

so

sin42)/31 = sin 86.1)/y

0.021 = 0.997 /y

y= 0.997/0.021 =47.47