anonymous176
16.10.2020 •
Mathematics
Three families bought food at the baseball game. The Smith family spent $16.50 on 3 hot dogs, 2 sodas, and 1 candy bar. The Patterson family spent $26 on 4 hot dogs, 4 sodas, and 2 candy bars. The Nguyen family spent $13.75 on 2 hot dogs, 1 soda, and 3 candy bars. Which of the following systems of equations could be used to determine the price of each item?
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Ответ:
Step-by-step explanation:
Let
Price of
Hotdogs = x
Sodas = y
Candy bar = z
Smith family
Hotdogs = 3
Sodas = 2
Candy bar = 1
Total cost = $16.50
3x + 2y + z = 16.50
Patterson family
Hotdogs = 4
Sodas = 4
Candy bar = 2
Total = $26
4x + 4y + 2z = 26
Nguyen family
Hotdogs = 2
Sodas = 1
Candy bar = 3
Total cost = $13.75
2x + y + 3z = 13.75
The equations
3x + 2y + z = 16.50 (1)
4x + 4y + 2z = 26 (2)
2x + y + 3z = 13.75 (3)
Multiply (1) by -2
-2(3x + 2y + z = 16.50)
-6x - 4y - 2z = -33
-6x - 4y - 2z = -33 (1a)
4x + 4y + 2z = 26 (2)
Add (1a) and (2)
-6x + 4x = -33 + 26
- 2x = -7
x = -7/-2
= 3.5
x = $3.5
Multiply (3) by -4
-4(2x + y + 3z = 13.75) (3)
-8x - 4y - 12z = -55 (3a)
Add (3a) and (2)
-8x - 4y - 12z = -55 (3a)
4x + 4y + 2z = 26 (2)
-8x + 4x -12z + 2z = -55 + 36
-4x - 10z = -29
Substitute the value of x into
-4x - 10z = -29
-4(3.5) - 10z = -29
-14 - 10z = -29
-10z = -29 + 14
-10z = - 15
z = -15 / - 10
= 1.5
z = $1.5
Substitute values of x and z into (1)
3x + 2y + z = 16.50
3(3.5) + 2y + 1.5 = 16.50
10.5 + 2y + 1.5 = 16.50
12 + 2y = 16.50
2y = 16.50 - 12
2y = 4.50
y = 4.50 / 2
y = $2.25
Ответ:
8320
Step-by-step explanation:
(100%+4%)8000=8320