Question

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

Answer 1

Joe bought 15 bags of chips and 8 bags of pretzels for the club meeting, as determined by solving a system of linear equations.

Step-by-step explanation:

The student is faced with a linear equation problem where the total amount spent on snacks and the total number of snacks are known, but the quantities of each type of snack are unknown. We can set up a system of equations to solve for the number of bags of chips and pretzels that Joe bought:

Let x be the number of bags of chips and y be the number of bags of pretzels. Therefore, we can establish the following equations based on the given information:

0.25x + 0.50y = 7.75 (This represents the total amount spent)

x + y = 23 (This represents the total number of snacks)

Now we can solve this system of equations using substitution or elimination methods. By multiplying the second equation by 0.25, we get:

0.25x + 0.25y = 5.75

If we subtract this new equation from the first equation, we have:

0.50y - 0.25y = 7.75 - 5.75

0.25y = 2

y = 8

Now that we have the value for y, we can substitute this back into the second equation to get:

x + 8 = 23

x = 23 - 8

x = 15

Thus, Joe bought 15 bags of chips and 8 bags of pretzels.

The correct answer is (d) 15 bags of chips; and 8 bags of pretzels.

Answer 2

Answer: D

`15` bags of chips;
`8` bags of pretzels

Step-by-step explanation:

1) Write the system of equations:
`\left \{ {{.25c+.50p=7.75} \atop {c+p=23}} \right.`

2) Multiply the first equation by -4,and multiply the second equation by 1:
`-4(0.25c+0.5p=7.75)`,
`1(c+p=23)`

3) Simplify:
`-c-2p=-31`,
`c+p=23`

4) Add the equations to eliminate c, then simplify:
`-p=8`

5) Divide both sides by
`-1`:
`(-p)/(-1) =(-8)/(-1)`

6) Simplify:
`p=8`

7) Rewrite equation and substitute
`8` for
`p` in
`0.25c+0.5p=7.75`:
`0.25c+(0.5)(8)=7.75`

8) Simplify:
`0.25c+4=7.75`

9) Subtract
`4` to both sides of the equation:
`0.25c+4-4=7.75-4`

10) Simplify:
`0.25c=3.75`

11) Divide both sides by
`0.25`:
`(0.25c)/(0.25) =(3.75)/(0.25)`

12) Simplify:
`c=15`

13) Write answer:
`15` bags of chips;
`8` bags of pretzels