Cost of each bags of flour = $2.50
Cost of each bags of butter = $3.75
Solution:
Let f be the bags of flour and b be the pounds of butter.
Cost of 20 bags of flour 16 pound of butter = 110
⇒ 20f + 16b = 110 -------------------- (1)
Cost of 30 bags of flour 12 pound of butter = 120
⇒ 30f + 12b = 120 -------------------- (2)
Equation (1) and (2) are the system of equations.
(2) ⇒ 30f + 12b = 120
Subtract 30f from both sides.
⇒ 12b = 120 – 30f
Divide by 12 on both sides.
[tex]$\Rightarrow b =\frac{120-30f}{12}[/tex] -------------------- (3)
Substitute (3) in (1).
[tex]$20f+16\left(\frac{120-30f}{12}\right)=110[/tex]
[tex]$20f+4\left(\frac{120-30f}{3}\right)=110[/tex]
[tex]$20f+4(40-10f)=110[/tex]
[tex]$20f+160-40f=110[/tex]
Subtract 160 from both sides.
[tex]$-20f=-50[/tex]
Divide by –20, we get
[tex]$f=\frac{5}{2}[/tex]
f = 2.50
Substitute f = 2.5 in equation (3), we get
[tex]$\Rightarrow b =\frac{120-30(2.50)}{12}[/tex]
[tex]$b=\frac{15}{4}[/tex]
b = 3.75
Cost of each bags of flour = $2.50
Cost of each bags of butter = $3.75
