Answer: D
[tex]15[/tex] bags of chips; [tex]8[/tex] bags of pretzels
Step-by-step explanation:
1) Write the system of equations: [tex]\left \{ {{.25c+.50p=7.75} \atop {c+p=23}} \right.[/tex]
2) Multiply the first equation by -4,and multiply the second equation by 1: [tex]-4(0.25c+0.5p=7.75)[/tex], [tex]1(c+p=23)[/tex]
3) Simplify: [tex]-c-2p=-31[/tex], [tex]c+p=23[/tex]
4) Add the equations to eliminate c, then simplify: [tex]-p=8[/tex]
5) Divide both sides by [tex]-1[/tex]: [tex]\frac{-p}{-1} =\frac{-8}{-1}[/tex]
6) Simplify: [tex]p=8[/tex]
7) Rewrite equation and substitute [tex]8[/tex] for [tex]p[/tex] in [tex]0.25c+0.5p=7.75[/tex]: [tex]0.25c+(0.5)(8)=7.75[/tex]
8) Simplify: [tex]0.25c+4=7.75[/tex]
9) Subtract [tex]4[/tex] to both sides of the equation: [tex]0.25c+4-4=7.75-4[/tex]
10) Simplify: [tex]0.25c=3.75[/tex]
11) Divide both sides by [tex]0.25[/tex]: [tex]\frac{0.25c}{0.25} =\frac{3.75}{0.25}[/tex]
12) Simplify: [tex]c=15[/tex]
13) Write answer: [tex]15[/tex] bags of chips; [tex]8[/tex] bags of pretzels
