2) The solutions for x and y in terms of each other are x = 77 - 2y and y = 38.5 - 0.5x respectively.
3) In the equation, c = 18.9 - 2.1r, it is equivalent to 0.9c + 1.89r = 17.01. Similarly, in the equation, r = -
+ 9, it is equivalent to 0.9c + 1.89r = 17.01.
2) Given Equation: 2x + 4y - 31 = 123
Variables = x and y
To solve for x, we rearrange the equation thus:
2x = 123 + 31 - 4y
x = (154 - 4y) ÷ 2
x = 77 - 2y
To solve the equation for y:
4y = 123 + 31 - 2x
y = (154 - 2x) /÷ 4
y = 38.5 - 0.5x
Thus, the solutions for x and y in terms of each other are x = 77 - 2y and y = 38.5 - 0.5x respectively.
3) The total cost of purchasing ribs and chicken = $17.01
The cost per pound of ribs = $1.89
The cost per pound of chicken = $0.90
Given equation:
0.9c + 1.89r = 17.01
a) Make c the subject of the equation by isolating it in the original equation:
0.9c = 17.01 - 1.89r
Divide all terms by 0.9:
c = 17.01 ÷ 0.9 - 1.89r ÷ 0.9
c = 18.9 - 2.1r
This equation is equivalent to 0.9c + 1.89r = 17.01.
b) Make r the subject of the equation by isolating it in the original equation:
0.9c = 17.01 - 1.89r
Divide all terms by 1.89:
r = 17.01/1.89 - 0.9c/1.89
r = 9 - 1/2.1c
r = 9 - 10/21c
r = -
+ 9
This equation is also equivalent to 0.9c + 1.89r = 17.01.
Thus, we write the equations in these forms when solving for one variable in terms of the other, especially if the chef wants to know how many ribs he can buy for a certain amount of chicken, and vice versa.