Answer:
The cost of a ribeye steak dinner is $18.60.
The cost of a grilled salmon dinner is $9.03.
Explanation:
let r be the cost of a ribeye steak dinner
let g be the cost of a grilled salmon dinner
Represent the two situations using equations:
12r + 39g = 575.53 (equation 1)
25r + 13g = 582.43 (equation 2)
The best method to use for this case is elimination, which is when you get rid of one of the variables by subtracting or adding.
Since the coefficients for "g" are 39 and 13, they can be eliminated if equation 2 was triple itself.
(25r + 13g = 582.43) X 3
= 75r + 39g = 1747.29 (new equation 2)
Subtract "equation 1" from "new equation 2"
. 75r + 39g = 1747.29
- 12r + 39g = 575.53
. 63r + 0g = 1171.76 <=we only deal with "r" because 0g is nothing
. 63r = 1171.76 <=divide both sides by 63 to isolate r
. r = 18.60 <=rounded from 18.599...
The cost of a ribeye steak dinner is $18.60.
Use any one of the equations to solve for "g", the cost of grilled salmon dinners. I will use equation 1.
12r + 39g = 575.53
Substitute r = 18.6
12(18.6) + 39g = 575.53 <=only one variable now
223.2 + 39g = 575.53 <=subtract 223.2 from both sides
39g = 352.33 <=divide both sides by 39 to isolate g
g = 9.03 <=rounded from 9.0341...
The cost of a grilled salmon dinner is $9.03.