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Joe spent $7.75 to purchase 23 snacks for the club meeting. Chips are $0.25 and pretzels are $0.50. How many of each type of snack did Joe buy?

a
12 bags of chips; 11 bags of pretzels
b
11 bags of chips; 12 bags of pretzels
c
8 bags of chips; 15 bags of pretzels
d
15 bags of chips; 8 bags of pretzels

Sagot :

2185030

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

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