Question

One angle measures 54 more degrees than 3 times another angle. The angles are supplementary. What are their
measures?
Some friends went to the local movie theater and bought four large buckets of popcorn and six boxes of càndy. The
total for the snacks was $46.50. The last time you were at the theater, you bought a large bucket of popcorn and a box of candy, and the total was $9.75. How much would 2 large buckets of popcorn and 3 boxes of candy cost?

Answer 1

part one:
54+4x=180
4x=126
x=31.5

one angle is 31.5 degrees, the other angle is 148.5 degrees

Answer 2

x = 54+3y
x + y = 180
Plug 54 + 3y in for x in the second equation.
54 + 3y + y = 180
54+4y =180
Subtract 54 from both sides
4y = 126
Divide both sides by 4
y = 31.5
x = 54 + 3(31.5) x= 148.5

4p + 6c = 46.50
p + c = 9.75 rewrite p =9.75 - c
Plug new equation into first equation.
4(9.75 - c) +6c = 46.50
39 -4c + 6c = 46.50
39 +2c = 46.50
Subtract 39 from both sides
2c = 7.50
Divide both sides by 2
c = 3.75
p + 3.75 = 9.75
p = 6
2p + 3c = ??
2(6) + 3(3.75)=
12 + 11.25 = 23.25